Theorem pm4.45 1013

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 881	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
2	1	pm4.71i 569	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:  dn1  1073