Theorem pm5.62 889

Description: Theorem *5.62 of [WhiteheadRussell] p. 125. (Contributed by Roy F. Longton, 21-Jun-2005.)

Assertion

Ref	Expression
pm5.62	⊢ (((φ ∧ ψ) ∨ ¬ ψ) ↔ (φ ∨ ¬ ψ))

Proof of Theorem pm5.62

Step	Hyp	Ref	Expression
1		exmid 404	. 2 ⊢ (ψ ∨ ¬ ψ)
2		ordir 835	. 2 ⊢ (((φ ∧ ψ) ∨ ¬ ψ) ↔ ((φ ∨ ¬ ψ) ∧ (ψ ∨ ¬ ψ)))
3	1, 2	mpbiran2 885	1 ⊢ (((φ ∧ ψ) ∨ ¬ ψ) ↔ (φ ∨ ¬ ψ))

Syntax hints:  ¬ wn 3   ↔ wb 176   ∨ wo 357   ∧ wa 358

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360

This theorem is referenced by: (None)