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Theorem e22an 28444
Description: Conjunction form of e22 28443. (Contributed by Alan Sare, 11-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e22an.1  |-  (. ph ,. ps  ->.  ch ).
e22an.2  |-  (. ph ,. ps  ->.  th ).
e22an.3  |-  ( ( ch  /\  th )  ->  ta )
Assertion
Ref Expression
e22an  |-  (. ph ,. ps  ->.  ta ).

Proof of Theorem e22an
StepHypRef Expression
1 e22an.1 . 2  |-  (. ph ,. ps  ->.  ch ).
2 e22an.2 . 2  |-  (. ph ,. ps  ->.  th ).
3 e22an.3 . . 3  |-  ( ( ch  /\  th )  ->  ta )
43ex 423 . 2  |-  ( ch 
->  ( th  ->  ta ) )
51, 2, 4e22 28443 1  |-  (. ph ,. ps  ->.  ta ).
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   (.wvd2 28346
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  df-vd2 28347
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