import logic theorem tst (a b : Prop) (H : a ↔ b) : b ↔ a := have H1 : a → b, -- We need to mark H1 as fact, otherwise it is not visible by tactics from iff.elim_left H, by apply iff.intro; intro Hb; apply (iff.elim_right H Hb); intro Ha; apply (H1 Ha) theorem tst2 (a b : Prop) (H : a ↔ b) : b ↔ a := have H1 : a → b, from iff.elim_left H, begin apply iff.intro, intro Hb; apply (iff.elim_right H Hb), intro Ha; apply (H1 Ha) end