Theorem pm4.45 698

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 633	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
2	1	pm4.71i 371	1 ⊢ (𝜑 ↔ (𝜑 ∧ (𝜑 ∨ 𝜓)))

Syntax hints:   ∧ wa 97   ↔ wb 98   ∨ wo 629

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  dn1dc  867