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  7030  funcestrcsetclem7  18158  funcsetcestrclem7  18173  lmodvsdi  20842  lmodvsdir  20843  lmodvsass  20844  lss0cl  20904  phlpropd  21615  chpdmatlem3  22778  mbfimasn  25585  slmdvsdi  33212  slmdvsdir  33213  slmdvsass  33214  metider  33925  funcringcsetcALTV2lem7  48271  funcringcsetclem7ALTV  48294