ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3anidm12 GIF version

Theorem 3anidm12 1273
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 1184 . 2 (𝜑 → ((𝜑𝜓) → 𝜒))
32anabsi5 568 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 962
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 964
This theorem is referenced by:  3anidm13  1274  syl2an3an  1276  prarloclemarch2  7234  nq02m  7280  recexprlem1ssl  7448  recexprlem1ssu  7449  nncan  7998  dividap  8468  modqid0  10130  subsq  10406  retanclap  11436  tannegap  11442  gcd0id  11674  coprm  11829
  Copyright terms: Public domain W3C validator