Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ee333 Structured version   Unicode version

Theorem ee333 28663
Description: e333 28919 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee333.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
ee333.2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
ee333.3  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )
ee333.4  |-  ( th 
->  ( ta  ->  ( et  ->  ze ) ) )
Assertion
Ref Expression
ee333  |-  ( ph  ->  ( ps  ->  ( ch  ->  ze ) ) )

Proof of Theorem ee333
StepHypRef Expression
1 ee333.1 . . . 4  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
213imp 1148 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
3 ee333.2 . . . 4  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
433imp 1148 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  ta )
5 ee333.3 . . . 4  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )
653imp 1148 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  et )
7 ee333.4 . . 3  |-  ( th 
->  ( ta  ->  ( et  ->  ze ) ) )
82, 4, 6, 7syl3c 60 . 2  |-  ( (
ph  /\  ps  /\  ch )  ->  ze )
983exp 1153 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ze ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 937
This theorem is referenced by:  ee323  28664  ee123  28949
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 179  df-an 362  df-3an 939
  Copyright terms: Public domain W3C validator