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Theorem mpd3an23 1349
Description: An inference based on modus ponens. (Contributed by NM, 4-Dec-2006.)
Hypotheses
Ref Expression
mpd3an23.1 (𝜑𝜓)
mpd3an23.2 (𝜑𝜒)
mpd3an23.3 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
mpd3an23 (𝜑𝜃)

Proof of Theorem mpd3an23
StepHypRef Expression
1 id 19 . 2 (𝜑𝜑)
2 mpd3an23.1 . 2 (𝜑𝜓)
3 mpd3an23.2 . 2 (𝜑𝜒)
4 mpd3an23.3 . 2 ((𝜑𝜓𝜒) → 𝜃)
51, 2, 3, 4syl3anc 1248 1 (𝜑𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 979
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 981
This theorem is referenced by:  exp0  10538  bcpasc  10760  bccl  10761  pw2dvds  12180  qnumdencoprm  12207  qeqnumdivden  12208  grpinvid  12965  ghmid  13144  mgpvalg  13232  mgpex  13234  opprex  13378  unitgrpid  13423  qusmul2  13773  dvef  14541
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