Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ee221 Structured version   Unicode version

Theorem ee221 36882
Description: e221 36881 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee221.1  |-  ( ph  ->  ( ps  ->  ch ) )
ee221.2  |-  ( ph  ->  ( ps  ->  th )
)
ee221.3  |-  ( ph  ->  ta )
ee221.4  |-  ( ch 
->  ( th  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
ee221  |-  ( ph  ->  ( ps  ->  et ) )

Proof of Theorem ee221
StepHypRef Expression
1 ee221.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 ee221.2 . 2  |-  ( ph  ->  ( ps  ->  th )
)
3 ee221.3 . . 3  |-  ( ph  ->  ta )
43a1d 26 . 2  |-  ( ph  ->  ( ps  ->  ta ) )
5 ee221.4 . 2  |-  ( ch 
->  ( th  ->  ( ta  ->  et ) ) )
61, 2, 4, 5ee222 36710 1  |-  ( ph  ->  ( ps  ->  et ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4
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 188  df-an 372
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator