Theorem pm4.43 893

Description: Theorem *4.43 of [WhiteheadRussell] p. 119. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 26-Nov-2012.)

Assertion

Ref	Expression
pm4.43	⊢ (φ ↔ ((φ ∨ ψ) ∧ (φ ∨ ¬ ψ)))

Proof of Theorem pm4.43

Step	Hyp	Ref	Expression
1		pm3.24 852	. . 3 ⊢ ¬ (ψ ∧ ¬ ψ)
2	1	biorfi 396	. 2 ⊢ (φ ↔ (φ ∨ (ψ ∧ ¬ ψ)))
3		ordi 834	. 2 ⊢ ((φ ∨ (ψ ∧ ¬ ψ)) ↔ ((φ ∨ ψ) ∧ (φ ∨ ¬ ψ)))
4	2, 3	bitri 240	1 ⊢ (φ ↔ ((φ ∨ ψ) ∧ (φ ∨ ¬ ψ)))

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

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

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

This theorem is referenced by: (None)