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Theorem anandis 581
Description: Inference that undistributes conjunction in the antecedent. (Contributed by NM, 7-Jun-2004.)
Hypothesis
Ref Expression
anandis.1 (((𝜑𝜓) ∧ (𝜑𝜒)) → 𝜏)
Assertion
Ref Expression
anandis ((𝜑 ∧ (𝜓𝜒)) → 𝜏)

Proof of Theorem anandis
StepHypRef Expression
1 anandis.1 . . 3 (((𝜑𝜓) ∧ (𝜑𝜒)) → 𝜏)
21an4s 577 . 2 (((𝜑𝜑) ∧ (𝜓𝜒)) → 𝜏)
32anabsan 564 1 ((𝜑 ∧ (𝜓𝜒)) → 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:  3impdi  1271  dff13  5669  f1oiso  5727  ltapig  7153  ltmpig  7154  faclbnd  10494  tgcl  12243
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