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Theorem ee30 28520
Description: e30 28519 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee30.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
ee30.2  |-  ta
ee30.3  |-  ( th 
->  ( ta  ->  et ) )
Assertion
Ref Expression
ee30  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )

Proof of Theorem ee30
StepHypRef Expression
1 ee30.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
2 ee30.2 . . . . 5  |-  ta
32a1i 10 . . . 4  |-  ( ch 
->  ta )
43a1i 10 . . 3  |-  ( ps 
->  ( ch  ->  ta ) )
54a1i 10 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
6 ee30.3 . 2  |-  ( th 
->  ( ta  ->  et ) )
71, 5, 6ee33 28284 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  ee30an  28522
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
  Copyright terms: Public domain W3C validator