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))

This proof depends on syntax axioms:   → wi 4   ↔ wb 105

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  imim21b  253  nfabdw  2411  elabgt  2967  sbceqal  3107  dffun8  5405  ordiso2  7375  indstr2  10011  dfgcd2  12793