Theorem pm4.44 560

Description: Theorem *4.44 of [WhiteheadRussell] p. 119. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.44	⊢ (φ ↔ (φ ∨ (φ ∧ ψ)))

Proof of Theorem pm4.44

Step	Hyp	Ref	Expression
1		orc 374	. 2 ⊢ (φ → (φ ∨ (φ ∧ ψ)))
2		id 19	. . 3 ⊢ (φ → φ)
3		simpl 443	. . 3 ⊢ ((φ ∧ ψ) → φ)
4	2, 3	jaoi 368	. 2 ⊢ ((φ ∨ (φ ∧ ψ)) → φ)
5	1, 4	impbii 180	1 ⊢ (φ ↔ (φ ∨ (φ ∧ ψ)))

Syntax hints:   ↔ 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)