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Theorem mpd3an23 1245
Description: An inference based on modus ponens. (Contributed by NM, 4-Dec-2006.)
Hypotheses
Ref Expression
mpd3an23.1  |-  ( ph  ->  ps )
mpd3an23.2  |-  ( ph  ->  ch )
mpd3an23.3  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
Assertion
Ref Expression
mpd3an23  |-  ( ph  ->  th )

Proof of Theorem mpd3an23
StepHypRef Expression
1 id 19 . 2  |-  ( ph  ->  ph )
2 mpd3an23.1 . 2  |-  ( ph  ->  ps )
3 mpd3an23.2 . 2  |-  ( ph  ->  ch )
4 mpd3an23.3 . 2  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
51, 2, 3, 4syl3anc 1146 1  |-  ( ph  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  exp0  9424  bcpasc  9634  bccl  9635  pw2dvds  10254
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