Theorem pm5.36 542

Description: Theorem *5.36 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.36	⊢ ((𝜑 ∧ (𝜑 ↔ 𝜓)) ↔ (𝜓 ∧ (𝜑 ↔ 𝜓)))

Proof of Theorem pm5.36

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 ↔ 𝜓))
2	1	pm5.32ri 428	1 ⊢ ((𝜑 ∧ (𝜑 ↔ 𝜓)) ↔ (𝜓 ∧ (𝜑 ↔ 𝜓)))

Syntax hints:   ∧ wa 97   ↔ wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by: (None)