Theorem anabss4 680

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 679	. 2 ⊢ ((𝜓 ∧ 𝜑) → 𝜒)
3	2	ancoms 464	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  anabss7  686  ordtri3or  6397