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Theorem 3anidm12 1415
 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 1118 . 2 (𝜑 → ((𝜑𝜓) → 𝜒))
32anabsi5 667 1 ((𝜑𝜓) → 𝜒)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 398   ∧ w3a 1083 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem depends on definitions:  df-bi 209  df-an 399  df-3an 1085 This theorem is referenced by:  3anidm13  1416  syl2an3an  1418  dedth3v  4531  nncan  10918  divid  11330  sqdivid  13491  subsq  13575  o1lo1  14897  retancl  15498  tanneg  15504  gcd0id  15870  coprm  16058  ablonncan  28336  kbpj  29736  xdivid  30608  xrsmulgzz  30669  f1resrcmplf1dlem  32363  expgrowthi  40671  dvconstbi  40672  3ornot23  40849  3anidm12p2  41147  sinhpcosh  44846  reseccl  44859  recsccl  44860  recotcl  44861  onetansqsecsq  44867
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