Theorem orabs 1000

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 867	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
2	1	pm4.71ri 560	1 ⊢ (𝜑 ↔ ((𝜑 ∨ 𝜓) ∧ 𝜑))

Syntax hints:   ↔ wb 206   ∧ wa 395   ∨ wo 847

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848

This theorem is referenced by: (None)