Theorem anabss4 511

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.)

Hypothesis

Ref	Expression
anabss4.1	⊢ (((𝜓 ∧ 𝜑) ∧ 𝜓) → 𝜒)

Assertion

Ref	Expression
anabss4	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Proof of Theorem anabss4

Step	Hyp	Ref	Expression
1		anabss4.1	. . 3 ⊢ (((𝜓 ∧ 𝜑) ∧ 𝜓) → 𝜒)
2	1	anabss1 510	. 2 ⊢ ((𝜓 ∧ 𝜑) → 𝜒)
3	2	ancoms 255	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 97

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:  anabss7  517