Theorem pm4.45 724

Description: Theorem *4.45 of [WhiteheadRussell] p. 119. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.45	⊢ (𝜑 ↔ (𝜑 ∧ (𝜑 ∨ 𝜓)))

Proof of Theorem pm4.45

Step	Hyp	Ref	Expression
1		orc 400	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
2	1	pm4.71i 664	1 ⊢ (𝜑 ↔ (𝜑 ∧ (𝜑 ∨ 𝜓)))

Syntax hints:   ↔ wb 196   ∨ wo 383   ∧ wa 384

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 197  df-or 385  df-an 386

This theorem is referenced by:  dn1  1008