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Theorem anandirs 582
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 577 . 2 (((𝜑𝜓) ∧ (𝜒𝜒)) → 𝜏)
32anabsan2 573 1 (((𝜑𝜓) ∧ 𝜒) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  3impdir  1272  fvreseq  5524  phplem4  6749  muladd  8158  iccshftr  9789  iccshftl  9791  iccdil  9793  icccntr  9795  fzaddel  9851  fzsubel  9852  mulexp  10344  upxp  12455  uptx  12457
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