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Theorem anabsan2 673
Description: Absorption of antecedent with conjunction. (Contributed by NM, 10-May-2004.)
Hypothesis
Ref Expression
anabsan2.1 ((𝜑 ∧ (𝜓𝜓)) → 𝜒)
Assertion
Ref Expression
anabsan2 ((𝜑𝜓) → 𝜒)

Proof of Theorem anabsan2
StepHypRef Expression
1 anabsan2.1 . . 3 ((𝜑 ∧ (𝜓𝜓)) → 𝜒)
21an12s 648 . 2 ((𝜓 ∧ (𝜑𝜓)) → 𝜒)
32anabss7 672 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397
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 398
This theorem is referenced by:  anabss3  674  anandirs  678  fvreseq  7037  funcestrcsetclem7  18094  funcsetcestrclem7  18109  lmodvsdi  20483  lmodvsdir  20484  lmodvsass  20485  lss0cl  20545  phlpropd  21192  chpdmatlem3  22324  mbfimasn  25131  slmdvsdi  32338  slmdvsdir  32339  slmdvsass  32340  metider  32812  funcringcsetcALTV2lem7  46842  funcringcsetclem7ALTV  46865
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