Theorem pm4.44 1012

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 881	. 2 ⊢ (𝜑 → (𝜑 ∨ (𝜑 ∧ 𝜓)))
2		id 23	. . 3 ⊢ (𝜑 → 𝜑)
3		simpl 488	. . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)
4	2, 3	jaoi 871	. 2 ⊢ ((𝜑 ∨ (𝜑 ∧ 𝜓)) → 𝜑)
5	1, 4	impbii 212	1 ⊢ (𝜑 ↔ (𝜑 ∨ (𝜑 ∧ 𝜓)))

This proof depends on syntax axioms:   ↔ wb 209   ∧ wa 401   ∨ wo 861

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

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862

This theorem is used by: (None)