Theorem anabsi6 670

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 465	. 2 ⊢ (𝜑 → ((𝜑 ∧ 𝜓) → 𝜒))
3	2	anabsi5 669	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 395

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396

This theorem is referenced by:  anabsi7  671  pjnormssi  32188  funressndmafv2rn  47240