Theorem anabss7 669

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 19-Nov-2013.)

Hypothesis

Ref	Expression
anabss7.1	⊢ ((𝜓 ∧ (𝜑 ∧ 𝜓)) → 𝜒)

Assertion

Ref	Expression
anabss7	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Proof of Theorem anabss7

Step	Hyp	Ref	Expression
1		anabss7.1	. . 3 ⊢ ((𝜓 ∧ (𝜑 ∧ 𝜓)) → 𝜒)
2	1	anassrs 467	. 2 ⊢ (((𝜓 ∧ 𝜑) ∧ 𝜓) → 𝜒)
3	2	anabss4 663	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 206  df-an 396

This theorem is referenced by:  anabsan2  670  syl2an23an  1421  funbrfv  6814  faclbnd5  13993  lcmcllem  16282  funbrafv2  44690