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Theorem jcai 523
Description: Deduction replacing implication with conjunction. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
jcai.1  |-  ( ph  ->  ps )
jcai.2  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
jcai  |-  ( ph  ->  ( ps  /\  ch ) )

Proof of Theorem jcai
StepHypRef Expression
1 jcai.1 . 2  |-  ( ph  ->  ps )
2 jcai.2 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
31, 2mpd 15 . 2  |-  ( ph  ->  ch )
41, 3jca 519 1  |-  ( ph  ->  ( ps  /\  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359
This theorem is referenced by:  reu6  3083  f1ocnv2d  6254  onfin2  7257  mpfrcl  19892  f1o3d  23994  altopthsn  25710  volsupnfl  26150  mbfresfi  26152  qirropth  26861
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 178  df-an 361
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