Theorem pm5.36 849

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 619	1 ⊢ ((φ ∧ (φ ↔ ψ)) ↔ (ψ ∧ (φ ↔ ψ)))

This proof depends on syntax axioms:   ↔ wb 176   ∧ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by: (None)