Theorem anabsan2 674

Description: Absorption of antecedent with conjunction. (Contributed by NM, 10-May-2004.)

Hypothesis

Ref	Expression
anabsan2.1	⊢ ((𝜑 ∧ (𝜓 ∧ 𝜓)) → 𝜒)

Assertion

Ref	Expression
anabsan2	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Proof of Theorem anabsan2

Step	Hyp	Ref	Expression
1		anabsan2.1	. . 3 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜓)) → 𝜒)
2	1	an12s 649	. 2 ⊢ ((𝜓 ∧ (𝜑 ∧ 𝜓)) → 𝜒)
3	2	anabss7 673	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:  anabss3  675  anandirs  679  fvreseq  7040  funcestrcsetclem7  18162  funcsetcestrclem7  18177  lmodvsdi  20852  lmodvsdir  20853  lmodvsass  20854  lss0cl  20914  phlpropd  21628  chpdmatlem3  22795  mbfimasn  25604  slmdvsdi  33165  slmdvsdir  33166  slmdvsass  33167  metider  33868  funcringcsetcALTV2lem7  48185  funcringcsetclem7ALTV  48208