- ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP X.∀_:theoremP (implies Y X).theoremP Y.∀H1:∀X:Univ.∀_:theoremP X.axiomP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or p q) (implies (or p (not q)) p))
+ ∀Univ:Set.∀A:Univ.∀B:Univ.∀C:Univ.∀X:Univ.∀Y:Univ.∀axiomP:∀_:Univ.Prop.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀or:∀_:Univ.∀_:Univ.Univ.∀p:Univ.∀q:Univ.∀theoremP:∀_:Univ.Prop.∀H0:∀X:Univ.∀Y:Univ.∀_:theoremP Y.∀_:theoremP (implies Y X).theoremP X.∀H1:∀X:Univ.∀_:axiomP X.theoremP X.∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (or (not X) Y).∀H3:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (implies A B) (implies (or C A) (or C B))).∀H4:∀A:Univ.∀B:Univ.∀C:Univ.axiomP (implies (or A (or B C)) (or B (or A C))).∀H5:∀A:Univ.∀B:Univ.axiomP (implies (or A B) (or B A)).∀H6:∀A:Univ.∀B:Univ.axiomP (implies A (or B A)).∀H7:∀A:Univ.axiomP (implies (or A A) A).theoremP (implies (or p q) (implies (or p (not q)) p))