Theorem anabss4 788

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 787	. 2 ⊢ ((ψ ∧ φ) → χ)
3	2	ancoms 439	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:  anabss7  794