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Theorem 3anidm13 1420
Description: Inference from idempotent law for conjunction. (Contributed by NM, 7-Mar-2008.)
Hypothesis
Ref Expression
3anidm13.1 ((𝜑𝜓𝜑) → 𝜒)
Assertion
Ref Expression
3anidm13 ((𝜑𝜓) → 𝜒)

Proof of Theorem 3anidm13
StepHypRef Expression
1 3anidm13.1 . . 3 ((𝜑𝜓𝜑) → 𝜒)
213com23 1126 . 2 ((𝜑𝜑𝜓) → 𝜒)
323anidm12 1419 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  w3a 1087
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 206  df-an 397  df-3an 1089
This theorem is referenced by:  npncan2  11424  ltsubpos  11643  leaddle0  11666  subge02  11667  halfaddsub  12382  avglt1  12387  hashssdif  14304  pythagtriplem4  16683  pythagtriplem14  16692  lsmss2  19440  grpoidinvlem2  29333  hvpncan3  29870  bcm1n  31581  revpfxsfxrev  33578  nnproddivdvdsd  40425  resubidaddid1  40802  reposdif  40850  3anidm12p1  43030  3impcombi  43041
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