Theorem anabsi8 546

Description: Absorption of antecedent into conjunction. (Contributed by NM, 26-Sep-1999.)

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 543	. 2 ⊢ ((𝜓 ∧ 𝜑) → 𝜒)
3	2	ancoms 264	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by: (None)