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Theorem ee30an 28522
Description: Conjunction form of ee30 28520. (Contributed by Alan Sare, 17-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee30an.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
ee30an.2  |-  ta
ee30an.3  |-  ( ( th  /\  ta )  ->  et )
Assertion
Ref Expression
ee30an  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )

Proof of Theorem ee30an
StepHypRef Expression
1 ee30an.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
2 ee30an.2 . 2  |-  ta
3 ee30an.3 . . 3  |-  ( ( th  /\  ta )  ->  et )
43ex 423 . 2  |-  ( th 
->  ( ta  ->  et ) )
51, 2, 4ee30 28520 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )
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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