Theorem pm5.501 330

Description: Theorem *5.501 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.501	⊢ (φ → (ψ ↔ (φ ↔ ψ)))

Proof of Theorem pm5.501

Step	Hyp	Ref	Expression
1		pm5.1im 229	. 2 ⊢ (φ → (ψ → (φ ↔ ψ)))
2		bi1 178	. . 3 ⊢ ((φ ↔ ψ) → (φ → ψ))
3	2	com12 27	. 2 ⊢ (φ → ((φ ↔ ψ) → ψ))
4	1, 3	impbid 183	1 ⊢ (φ → (ψ ↔ (φ ↔ ψ)))

This proof depends on syntax axioms:   → wi 4   ↔ wb 176

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177

This theorem is used by:  ibib  331  ibibr  332  nbn2  334  pm5.18  345  biass  348  pm5.1  830