Theorem anabs7 785

Description: Absorption into embedded conjunct. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 17-Nov-2013.)

Assertion

Ref	Expression
anabs7	⊢ ((ψ ∧ (φ ∧ ψ)) ↔ (φ ∧ ψ))

Proof of Theorem anabs7

Step	Hyp	Ref	Expression
1		simpr 447	. . 3 ⊢ ((φ ∧ ψ) → ψ)
2	1	pm4.71ri 614	. 2 ⊢ ((φ ∧ ψ) ↔ (ψ ∧ (φ ∧ ψ)))
3	2	bicomi 193	1 ⊢ ((ψ ∧ (φ ∧ ψ)) ↔ (φ ∧ ψ))

Syntax hints:   ↔ wb 176   ∧ 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-an 360

This theorem is referenced by: (None)