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  6968  funcestrcsetclem7  18047  funcsetcestrclem7  18062  lmodvsdi  20813  lmodvsdir  20814  lmodvsass  20815  lss0cl  20875  phlpropd  21587  chpdmatlem3  22750  mbfimasn  25555  slmdvsdi  33176  slmdvsdir  33177  slmdvsass  33178  metider  33899  funcringcsetcALTV2lem7  48327  funcringcsetclem7ALTV  48350