Theorem anabsi6 570

Description: Absorption of antecedent into conjunction. (Contributed by NM, 14-Aug-2000.)

Hypothesis

Ref	Expression
anabsi6.1	⊢ (𝜑 → ((𝜓 ∧ 𝜑) → 𝜒))

Assertion

Ref	Expression
anabsi6	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Proof of Theorem anabsi6

Step	Hyp	Ref	Expression
1		anabsi6.1	. . 3 ⊢ (𝜑 → ((𝜓 ∧ 𝜑) → 𝜒))
2	1	ancomsd 267	. 2 ⊢ (𝜑 → ((𝜑 ∧ 𝜓) → 𝜒))
3	2	anabsi5 569	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  anabsi7  571