Theorem anabsan2 795

Description: Absorption of antecedent with conjunction. (Contributed by NM, 10-May-2004.)

Hypothesis

Ref	Expression
anabsan2.1	⊢ ((φ ∧ (ψ ∧ ψ)) → χ)

Assertion

Ref	Expression
anabsan2	⊢ ((φ ∧ ψ) → χ)

Proof of Theorem anabsan2

Step	Hyp	Ref	Expression
1		anabsan2.1	. . 3 ⊢ ((φ ∧ (ψ ∧ ψ)) → χ)
2	1	an12s 776	. 2 ⊢ ((ψ ∧ (φ ∧ ψ)) → χ)
3	2	anabss7 794	1 ⊢ ((φ ∧ ψ) → χ)

This proof depends on syntax axioms:   → wi 4   ∧ wa 358

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

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by:  anabss3  796  anandirs  804