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Theorem 3adant2r 1179
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 482 . 2 ((𝜓𝜏) → 𝜓)
2 ad4ant3.1 . 2 ((𝜑𝜓𝜒) → 𝜃)
31, 2syl3an2 1164 1 ((𝜑 ∧ (𝜓𝜏) ∧ 𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  w3a 1086
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 207  df-an 396  df-3an 1088
This theorem is referenced by:  ltdiv23  12160  lediv23  12161  divalglem8  16438  isdrngd  20766  isdrngdOLD  20768  deg1tm  26159  ax5seglem1  28944  ax5seglem2  28945  nvaddsub4  30677  nmoub2i  30794  cdleme21at  40331  cdleme42f  40483  trlcoabs2N  40725  tendoplcl2  40781  tendopltp  40783  cdlemk2  40835  cdlemk8  40841  cdlemk9  40842  cdlemk9bN  40843  cdleml8  40986  dihglblem3N  41298  dihglblem3aN  41299  fourierdlem42  46169  lincscm  48352  itsclc0yqsol  48690
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