Theorem pm5.5 241

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 240	. 2 ⊢ (𝜑 → (𝜓 ↔ (𝜑 → 𝜓)))
2	1	bicomd 140	1 ⊢ (𝜑 → ((𝜑 → 𝜓) ↔ 𝜓))

Syntax hints:   → wi 4   ↔ wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  imim21b  251  nfabdw  2327  elabgt  2867  sbceqal  3006  dffun8  5216  ordiso2  7000  indstr2  9547  dfgcd2  11947