Theorem anabsan 663

Description: Absorption of antecedent with conjunction. (Contributed by NM, 24-Mar-1996.)

Hypothesis

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

Assertion

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

Proof of Theorem anabsan

Step	Hyp	Ref	Expression
1		pm4.24 566	. 2 ⊢ (𝜑 ↔ (𝜑 ∧ 𝜑))
2		anabsan.1	. 2 ⊢ (((𝜑 ∧ 𝜑) ∧ 𝜓) → 𝜒)
3	1, 2	sylanb 583	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 398

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 209  df-an 399

This theorem is referenced by:  anabss1  664  anabss5  666  anandis  676  iddvds  15617  1dvds  15618