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Theorem ee22an 28445
Description: e22an 28444 without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee22an.1  |-  ( ph  ->  ( ps  ->  ch ) )
ee22an.2  |-  ( ph  ->  ( ps  ->  th )
)
ee22an.3  |-  ( ( ch  /\  th )  ->  ta )
Assertion
Ref Expression
ee22an  |-  ( ph  ->  ( ps  ->  ta ) )

Proof of Theorem ee22an
StepHypRef Expression
1 ee22an.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 ee22an.2 . 2  |-  ( ph  ->  ( ps  ->  th )
)
3 ee22an.3 . . 3  |-  ( ( ch  /\  th )  ->  ta )
43ex 423 . 2  |-  ( ch 
->  ( th  ->  ta ) )
51, 2, 4ee22 1352 1  |-  ( ph  ->  ( ps  ->  ta ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
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