Theorem pm4.42 766

Description: Theorem *4.42 of [WhiteheadRussell] p. 119. (Contributed by Roy F. Longton, 21-Jun-2005.)

Assertion

Ref	Expression
pm4.42	⊢ (φ ↔ ((φ ⋀ ψ) ⋁ (φ ⋀ ¬ ψ)))

Proof of Theorem pm4.42

Step	Hyp	Ref	Expression
1		dedlema 760	. 2 ⊢ (ψ → (φ ↔ ((φ ⋀ ψ) ⋁ (φ ⋀ ¬ ψ))))
2		dedlemb 761	. 2 ⊢ (¬ ψ → (φ ↔ ((φ ⋀ ψ) ⋁ (φ ⋀ ¬ ψ))))
3	1, 2	pm2.61i 126	1 ⊢ (φ ↔ ((φ ⋀ ψ) ⋁ (φ ⋀ ¬ ψ)))

Syntax hints:  ¬ wn 2   ↔ wb 146   ⋁ wo 222   ⋀ wa 223

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225

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