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Theorem 3anidm12 1238
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 1149 . 2 (𝜑 → ((𝜑𝜓) → 𝜒))
32anabsi5 547 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 927
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 929
This theorem is referenced by:  3anidm13  1239  syl2an3an  1241  prarloclemarch2  7075  nq02m  7121  recexprlem1ssl  7289  recexprlem1ssu  7290  nncan  7808  dividap  8265  modqid0  9906  subsq  10176  retanclap  11162  tannegap  11168  gcd0id  11397  coprm  11550
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