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Theorem 3adant2r 1176
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 481 . 2 ((𝜓𝜏) → 𝜓)
2 ad4ant3.1 . 2 ((𝜑𝜓𝜒) → 𝜃)
31, 2syl3an2 1161 1 ((𝜑 ∧ (𝜓𝜏) ∧ 𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 394  w3a 1084
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 395  df-3an 1086
This theorem is referenced by:  ltdiv23  12157  lediv23  12158  divalglem8  16402  isdrngd  20743  isdrngdOLD  20745  deg1tm  26146  ax5seglem1  28862  ax5seglem2  28863  nvaddsub4  30590  nmoub2i  30707  cdleme21at  40027  cdleme42f  40179  trlcoabs2N  40421  tendoplcl2  40477  tendopltp  40479  cdlemk2  40531  cdlemk8  40537  cdlemk9  40538  cdlemk9bN  40539  cdleml8  40682  dihglblem3N  40994  dihglblem3aN  40995  fourierdlem42  45770  lincscm  47813  itsclc0yqsol  48152
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