ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  mp3an2ani Unicode version

Theorem mp3an2ani 1276
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 1275 . 2  |-  ( ( ps  /\  ( ps 
/\  th ) )  ->  et )
65anabss5 543 1  |-  ( ( ps  /\  th )  ->  et )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    /\ 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:  tfr1onlemubacc  6015  tfrcllemubacc  6028
  Copyright terms: Public domain W3C validator