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Theorem mp3an12i 1336
Description: mp3an 1332 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 1322 . 2 (𝜃𝜏)
61, 5syl 14 1 (𝜒𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 973
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 975
This theorem is referenced by:  map1  6790  suplocsrlempr  7769  geo2lim  11479  fprodge0  11600  fprodge1  11602  oddp1d2  11849  bezoutlema  11954  bezoutlemb  11955  pythagtriplem1  12219  exmidunben  12381  ismet  13138  isxmet  13139  coseq0negpitopi  13551  cosq34lt1  13565  cos02pilt1  13566  logdivlti  13596
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