Theorem anabs7 508

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 103	. . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	pm4.71ri 372	. 2 ⊢ ((𝜑 ∧ 𝜓) ↔ (𝜓 ∧ (𝜑 ∧ 𝜓)))
3	2	bicomi 123	1 ⊢ ((𝜓 ∧ (𝜑 ∧ 𝜓)) ↔ (𝜑 ∧ 𝜓))

Syntax hints:   ∧ wa 97   ↔ wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by: (None)