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Theorem 3anidm12 1306
Description: Inference from idempotent law for conjunction. (Contributed by NM, 7-Mar-2008.)
Hypothesis
Ref Expression
3anidm12.1 ((𝜑𝜑𝜓) → 𝜒)
Assertion
Ref Expression
3anidm12 ((𝜑𝜓) → 𝜒)

Proof of Theorem 3anidm12
StepHypRef Expression
1 3anidm12.1 . . 3 ((𝜑𝜑𝜓) → 𝜒)
213expib 1208 . 2 (𝜑 → ((𝜑𝜓) → 𝜒))
32anabsi5 579 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  w3a 980
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 982
This theorem is referenced by:  3anidm13  1307  syl2an3an  1309  fovcl  5997  prarloclemarch2  7437  nq02m  7483  recexprlem1ssl  7651  recexprlem1ssu  7652  nncan  8205  dividap  8677  modqid0  10369  sqdividap  10604  subsq  10646  retanclap  11749  tannegap  11755  gcd0id  11999  coprm  12163
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