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Theorem an42s 660
Description: Inference rearranging 4 conjuncts in antecedent. (Contributed by NM, 10-Aug-1995.)
Hypothesis
Ref Expression
an41r3s.1 (((𝜑𝜓) ∧ (𝜒𝜃)) → 𝜏)
Assertion
Ref Expression
an42s (((𝜑𝜒) ∧ (𝜃𝜓)) → 𝜏)

Proof of Theorem an42s
StepHypRef Expression
1 an41r3s.1 . . 3 (((𝜑𝜓) ∧ (𝜒𝜃)) → 𝜏)
21an4s 659 . 2 (((𝜑𝜒) ∧ (𝜓𝜃)) → 𝜏)
32ancom2s 649 1 (((𝜑𝜒) ∧ (𝜃𝜓)) → 𝜏)
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:  nnmsucr  8625  ecopoveq  8812  sbthlem9  9091  mulclsr  11079  mulasssr  11085  distrsr  11086  ltsosr  11089  axmulf  11141  axmulass  11152  axdistr  11153  subadd4  11504  mulsub  11657  mgmidmo  18579  tgcl  22472  bwth  22914  pntibndlem2  27094  hosubadd4  31067  pibt2  36298  lindsadd  36481  fdc  36613  isdrngo2  36826  unichnidl  36899  acongtr  41717
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