Theorem bitr3 354

Description: Closed nested implication form of bitr3i 279. Derived automatically from bitr3VD 45388. (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 353	. 2 ⊢ ((𝜑 ↔ 𝜓) → ((𝜑 ↔ 𝜒) ↔ (𝜓 ↔ 𝜒)))
2	1	biimpd 231	1 ⊢ ((𝜑 ↔ 𝜓) → ((𝜑 ↔ 𝜒) → (𝜓 ↔ 𝜒)))

Syntax hints:   → wi 4   ↔ wb 208

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 209

This theorem is referenced by:  imbibi  394  sumodd  16405  3orbi123VD  45389  sbc3orgVD  45390  trsbcVD  45416  csbrngVD  45435  e2ebindVD  45451  e2ebindALT  45468