Theorem pm5.5 240

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 239	. 2 ⊢ (𝜑 → (𝜓 ↔ (𝜑 → 𝜓)))
2	1	bicomd 139	1 ⊢ (𝜑 → ((𝜑 → 𝜓) ↔ 𝜓))

Syntax hints:   → wi 4   ↔ wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  imim21b  250  elabgt  2735  sbceqal  2869  dffun8  4949  ordiso2  6446  indstr2  8696  dfgcd2  10403