Theorem pm5.5 326

Description: Theorem *5.5 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.5	⊢ (φ → ((φ → ψ) ↔ ψ))

Proof of Theorem pm5.5

Step	Hyp	Ref	Expression
1		biimt 325	. 2 ⊢ (φ → (ψ ↔ (φ → ψ)))
2	1	bicomd 192	1 ⊢ (φ → ((φ → ψ) ↔ ψ))

Syntax hints:   → wi 4   ↔ wb 176

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 177

This theorem is referenced by:  imim21b  356  elabgt  2983  sbceqal  3098