Theorem pm5.5 242

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 241	. 2 ⊢ (𝜑 → (𝜓 ↔ (𝜑 → 𝜓)))
2	1	bicomd 141	1 ⊢ (𝜑 → ((𝜑 → 𝜓) ↔ 𝜓))

Syntax hints:   → wi 4   ↔ wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  imim21b  253  nfabdw  2338  elabgt  2880  sbceqal  3020  dffun8  5246  ordiso2  7036  indstr2  9611  dfgcd2  12017