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Theorem 3adant2r 1171
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.) (Proof shortened by Wolf Lammen, 25-Jun-2022.)
Hypothesis
Ref Expression
ad4ant3.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
3adant2r ((𝜑 ∧ (𝜓𝜏) ∧ 𝜒) → 𝜃)

Proof of Theorem 3adant2r
StepHypRef Expression
1 simpl 483 . 2 ((𝜓𝜏) → 𝜓)
2 ad4ant3.1 . 2 ((𝜑𝜓𝜒) → 𝜃)
31, 2syl3an2 1156 1 ((𝜑 ∧ (𝜓𝜏) ∧ 𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  w3a 1079
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 208  df-an 397  df-3an 1081
This theorem is referenced by:  ltdiv23  11519  lediv23  11520  divalglem8  15739  isdrngd  19456  deg1tm  24639  ax5seglem1  26641  ax5seglem2  26642  nvaddsub4  28361  nmoub2i  28478  cdleme21at  37344  cdleme42f  37496  trlcoabs2N  37738  tendoplcl2  37794  tendopltp  37796  cdlemk2  37848  cdlemk8  37854  cdlemk9  37855  cdlemk9bN  37856  cdleml8  37999  dihglblem3N  38311  dihglblem3aN  38312  fourierdlem42  42311  lincscm  44413  itsclc0yqsol  44679
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