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Theorem syl2an23an 1422
Description: Deduction related to syl3an 1159 with antecedents in standard conjunction form. (Contributed by Alan Sare, 31-Aug-2016.) (Proof shortened by Wolf Lammen, 28-Jun-2022.)
Hypotheses
Ref Expression
syl2an23an.1 (𝜑𝜓)
syl2an23an.2 (𝜑𝜒)
syl2an23an.3 ((𝜃𝜑) → 𝜏)
syl2an23an.4 ((𝜓𝜒𝜏) → 𝜂)
Assertion
Ref Expression
syl2an23an ((𝜃𝜑) → 𝜂)

Proof of Theorem syl2an23an
StepHypRef Expression
1 syl2an23an.1 . . 3 (𝜑𝜓)
2 syl2an23an.2 . . 3 (𝜑𝜒)
3 syl2an23an.3 . . 3 ((𝜃𝜑) → 𝜏)
4 syl2an23an.4 . . 3 ((𝜓𝜒𝜏) → 𝜂)
51, 2, 3, 4syl2an3an 1421 . 2 ((𝜑 ∧ (𝜃𝜑)) → 𝜂)
65anabss7 673 1 ((𝜃𝜑) → 𝜂)
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:  nf1const  7324  uztrn  12894  ssfzo12bi  13797  modsumfzodifsn  13982  facdiv  14323  swrdnd  14689  cshwidxmod  14838  nndivdvds  16296  pcz  16915  fldivp1  16931  uffix  23945  relogbmul  26835  umgrvad2edg  29245  crctcshwlkn0  29851  satfsschain  35349  satfdm  35354  satffunlem2  35393
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