Theorem anabss3 673

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 1-Jan-2013.)

Hypothesis

Ref	Expression
anabss3.1	⊢ (((𝜑 ∧ 𝜓) ∧ 𝜓) → 𝜒)

Assertion

Ref	Expression
anabss3	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Proof of Theorem anabss3

Step	Hyp	Ref	Expression
1		anabss3.1	. . 3 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜓) → 𝜒)
2	1	anasss 469	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜓)) → 𝜒)
3	2	anabsan2 672	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:  3anidm23  1417  expclzlem  13447  plyrem  24888  loop1cycl  32379  anabss7p1  41114