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Theorem mp3an12i 1341
Description: mp3an 1337 with antecedents in standard conjunction form and with one hypothesis an implication. (Contributed by Alan Sare, 28-Aug-2016.)
Hypotheses
Ref Expression
mp3an12i.1 𝜑
mp3an12i.2 𝜓
mp3an12i.3 (𝜒𝜃)
mp3an12i.4 ((𝜑𝜓𝜃) → 𝜏)
Assertion
Ref Expression
mp3an12i (𝜒𝜏)

Proof of Theorem mp3an12i
StepHypRef Expression
1 mp3an12i.3 . 2 (𝜒𝜃)
2 mp3an12i.1 . . 3 𝜑
3 mp3an12i.2 . . 3 𝜓
4 mp3an12i.4 . . 3 ((𝜑𝜓𝜃) → 𝜏)
52, 3, 4mp3an12 1327 . 2 (𝜃𝜏)
61, 5syl 14 1 (𝜒𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 980
This theorem is referenced by:  map1  6814  suplocsrlempr  7808  geo2lim  11526  fprodge0  11647  fprodge1  11649  oddp1d2  11897  bezoutlema  12002  bezoutlemb  12003  pythagtriplem1  12267  exmidunben  12429  ismet  13883  isxmet  13884  coseq0negpitopi  14296  cosq34lt1  14310  cos02pilt1  14311  logdivlti  14341  lgseisenlem1  14489  m1lgs  14491
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