Theorem anabsi8 380

Description: Absorption of antecedent into conjunction.

Hypothesis

Ref	Expression
anabsi8.1	⊢ (ψ → ((ψ ∧ φ) → χ))

Assertion

Ref	Expression
anabsi8	⊢ ((φ ∧ ψ) → χ)

Proof of Theorem anabsi8

Step	Hyp	Ref	Expression
1		anabsi8.1	. . 3 ⊢ (ψ → ((ψ ∧ φ) → χ))
2	1	anabsi5 377	. 2 ⊢ ((ψ ∧ φ) → χ)
3	2	ancoms 334	1 ⊢ ((φ ∧ ψ) → χ)

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  projlem1 5193

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

metamath.org