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Theorem mp3and 1272
Description: A deduction based on modus ponens. (Contributed by Mario Carneiro, 24-Dec-2016.)
Hypotheses
Ref Expression
mp3and.1  |-  ( ph  ->  ps )
mp3and.2  |-  ( ph  ->  ch )
mp3and.3  |-  ( ph  ->  th )
mp3and.4  |-  ( ph  ->  ( ( ps  /\  ch  /\  th )  ->  ta ) )
Assertion
Ref Expression
mp3and  |-  ( ph  ->  ta )

Proof of Theorem mp3and
StepHypRef Expression
1 mp3and.1 . . 3  |-  ( ph  ->  ps )
2 mp3and.2 . . 3  |-  ( ph  ->  ch )
3 mp3and.3 . . 3  |-  ( ph  ->  th )
41, 2, 33jca 1119 . 2  |-  ( ph  ->  ( ps  /\  ch  /\ 
th ) )
5 mp3and.4 . 2  |-  ( ph  ->  ( ( ps  /\  ch  /\  th )  ->  ta ) )
64, 5mpd 13 1  |-  ( ph  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by:  eqsuptid  6469  eqinftid  6493  bezoutlemsup  10542
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