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Theorem mp3an12i 1302
Description: mp3an 1298 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 1288 . 2 (𝜃𝜏)
61, 5syl 14 1 (𝜒𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 945
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 947
This theorem is referenced by:  map1  6672  suplocsrlempr  7579  geo2lim  11236  oddp1d2  11494  bezoutlema  11594  bezoutlemb  11595  exmidunben  11845  ismet  12419  isxmet  12420
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