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Theorem anandirs 527
Description: Inference that undistributes conjunction in the antecedent. (Contributed by NM, 7-Jun-2004.)
Hypothesis
Ref Expression
anandirs.1 (((𝜑𝜒) ∧ (𝜓𝜒)) → 𝜏)
Assertion
Ref Expression
anandirs (((𝜑𝜓) ∧ 𝜒) → 𝜏)

Proof of Theorem anandirs
StepHypRef Expression
1 anandirs.1 . . 3 (((𝜑𝜒) ∧ (𝜓𝜒)) → 𝜏)
21an4s 522 . 2 (((𝜑𝜓) ∧ (𝜒𝜒)) → 𝜏)
32anabsan2 518 1 (((𝜑𝜓) ∧ 𝜒) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  3impdir  1191  fvreseq  5258  phplem4  6305  muladd  7360  iccshftr  8829  iccshftl  8831  iccdil  8833  icccntr  8835  fzaddel  8889  fzsubel  8890  mulexp  9172
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