Theorem orabs 1014

Description: Absorption of redundant internal disjunct. Compare Theorem *4.45 of [WhiteheadRussell] p. 119. (Contributed by NM, 21-Jun-1993.) (Proof shortened by Wolf Lammen, 28-Feb-2014.)

Assertion

Ref	Expression
orabs	⊢ (𝜑 ↔ ((𝜑 ∨ 𝜓) ∧ 𝜑))

Proof of Theorem orabs

Step	Hyp	Ref	Expression
1		orc 881	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
2	1	pm4.71ri 570	1 ⊢ (𝜑 ↔ ((𝜑 ∨ 𝜓) ∧ 𝜑))

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: (None)