Theorem pm4.45 669

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 374	. 2 ⊢ (φ → (φ ∨ ψ))
2	1	pm4.71i 613	1 ⊢ (φ ↔ (φ ∧ (φ ∨ ψ)))

This proof depends on syntax axioms:   ↔ wb 176   ∨ wo 357   ∧ wa 358

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

This proof depends on definitions:  df-bi 177  df-or 359  df-an 360

This theorem is used by:  dn1  932