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  6985  funcestrcsetclem7  18069  funcsetcestrclem7  18084  lmodvsdi  20836  lmodvsdir  20837  lmodvsass  20838  lss0cl  20898  phlpropd  21610  chpdmatlem3  22784  mbfimasn  25589  slmdvsdi  33297  slmdvsdir  33298  slmdvsass  33299  metider  34051  funcringcsetcALTV2lem7  48542  funcringcsetclem7ALTV  48565