Theorem anabss4 504

Description: Absorption of antecedent into conjunction.

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 502	. 2 ⊢ ((ψ ⋀ φ) → χ)
3	2	ancoms 439	1 ⊢ ((φ ⋀ ψ) → χ)

Syntax hints:   → wi 3   ⋀ wa 223

This theorem is referenced by:  ordtri3or 2995

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

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