Theorem anabss7 385

Description: Absorption of antecedent into conjunction.

Hypothesis

Ref	Expression
anabss7.1	⊢ ((ψ ∧ (φ ∧ ψ)) → χ)

Assertion

Ref	Expression
anabss7	⊢ ((φ ∧ ψ) → χ)

Proof of Theorem anabss7

Step	Hyp	Ref	Expression
1		anabss7.1	. . 3 ⊢ ((ψ ∧ (φ ∧ ψ)) → χ)
2	1	exp 291	. 2 ⊢ (ψ → ((φ ∧ ψ) → χ))
3	2	anabsi7 379	1 ⊢ ((φ ∧ ψ) → χ)

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  funbrfv 2852

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

This theorem depends on definitions:  df-bi 128  df-an 198

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