Theorem bitr3 352

Description: Closed nested implication form of bitr3i 277. Derived automatically from bitr3VD 44820. (Contributed by Alan Sare, 31-Dec-2011.)

Assertion

Ref	Expression
bitr3	⊢ ((𝜑 ↔ 𝜓) → ((𝜑 ↔ 𝜒) → (𝜓 ↔ 𝜒)))

Proof of Theorem bitr3

Step	Hyp	Ref	Expression
1		bibi1 351	. 2 ⊢ ((𝜑 ↔ 𝜓) → ((𝜑 ↔ 𝜒) ↔ (𝜓 ↔ 𝜒)))
2	1	biimpd 229	1 ⊢ ((𝜑 ↔ 𝜓) → ((𝜑 ↔ 𝜒) → (𝜓 ↔ 𝜒)))

Syntax hints:   → wi 4   ↔ wb 206

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207

This theorem is referenced by:  sumodd  16436  3orbi123VD  44821  sbc3orgVD  44822  trsbcVD  44848  csbrngVD  44867  e2ebindVD  44883  e2ebindALT  44900