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Theorem mp3an2ani 1307
Description: An elimination deduction. (Contributed by Alan Sare, 17-Oct-2017.)
Hypotheses
Ref Expression
mp3an2ani.1  |-  ph
mp3an2ani.2  |-  ( ps 
->  ch )
mp3an2ani.3  |-  ( ( ps  /\  th )  ->  ta )
mp3an2ani.4  |-  ( (
ph  /\  ch  /\  ta )  ->  et )
Assertion
Ref Expression
mp3an2ani  |-  ( ( ps  /\  th )  ->  et )

Proof of Theorem mp3an2ani
StepHypRef Expression
1 mp3an2ani.1 . . 3  |-  ph
2 mp3an2ani.2 . . 3  |-  ( ps 
->  ch )
3 mp3an2ani.3 . . 3  |-  ( ( ps  /\  th )  ->  ta )
4 mp3an2ani.4 . . 3  |-  ( (
ph  /\  ch  /\  ta )  ->  et )
51, 2, 3, 4mp3an3an 1306 . 2  |-  ( ( ps  /\  ( ps 
/\  th ) )  ->  et )
65anabss5 552 1  |-  ( ( ps  /\  th )  ->  et )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 947
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 949
This theorem is referenced by:  tfr1onlemubacc  6211  tfrcllemubacc  6224  mappsrprg  7580  metrest  12602
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