Theorem pm4.25 919

Description: Theorem *4.25 of [WhiteheadRussell] p. 117. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.25	⊢ (𝜑 ↔ (𝜑 ∨ 𝜑))

Proof of Theorem pm4.25

Step	Hyp	Ref	Expression
1		oridm 918	. 2 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)
2	1	bicomi 227	1 ⊢ (𝜑 ↔ (𝜑 ∨ 𝜑))

This proof depends on syntax axioms:   ↔ wb 209   ∨ 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-or 862

This theorem is used by:  el.OLD  5407  brbtwn2  29483  ifpid1g  44494  uneqsn  45024  homf0  50116