Theorem orabs 828

Description: Absorption of redundant internal disjunct. Compare Theorem *4.45 of [WhiteheadRussell] p. 119. (Contributed by NM, 5-Aug-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 374	. 2 ⊢ (φ → (φ ∨ ψ))
2	1	pm4.71ri 614	1 ⊢ (φ ↔ ((φ ∨ ψ) ∧ φ))

Syntax hints:   ↔ wb 176   ∨ wo 357   ∧ wa 358

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 177  df-or 359  df-an 360

This theorem is referenced by: (None)