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Theorem 3anidm12 1290
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 1201 . 2 (𝜑 → ((𝜑𝜓) → 𝜒))
32anabsi5 574 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 973
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  df-3an 975
This theorem is referenced by:  3anidm13  1291  syl2an3an  1293  prarloclemarch2  7381  nq02m  7427  recexprlem1ssl  7595  recexprlem1ssu  7596  nncan  8148  dividap  8618  modqid0  10306  subsq  10582  retanclap  11685  tannegap  11691  gcd0id  11934  coprm  12098
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