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Theorem ee220 36870
Description: e220 36869 without virtual deductions. (Contributed by Alan Sare, 12-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee220.1  |-  ( ph  ->  ( ps  ->  ch ) )
ee220.2  |-  ( ph  ->  ( ps  ->  th )
)
ee220.3  |-  ta
ee220.4  |-  ( ch 
->  ( th  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
ee220  |-  ( ph  ->  ( ps  ->  et ) )

Proof of Theorem ee220
StepHypRef Expression
1 ee220.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 ee220.2 . 2  |-  ( ph  ->  ( ps  ->  th )
)
3 ee220.3 . . 3  |-  ta
432a1i 12 . 2  |-  ( ph  ->  ( ps  ->  ta ) )
5 ee220.4 . 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