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Theorem mprg 2395
Description: Modus ponens combined with restricted generalization. (Contributed by NM, 10-Aug-2004.)
Hypotheses
Ref Expression
mprg.1  |-  ( A. x  e.  A  ph  ->  ps )
mprg.2  |-  ( x  e.  A  ->  ph )
Assertion
Ref Expression
mprg  |-  ps

Proof of Theorem mprg
StepHypRef Expression
1 mprg.2 . . 3  |-  ( x  e.  A  ->  ph )
21rgen 2391 . 2  |-  A. x  e.  A  ph
3 mprg.1 . 2  |-  ( A. x  e.  A  ph  ->  ps )
42, 3ax-mp 7 1  |-  ps
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1409   A.wral 2323
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-gen 1354
This theorem depends on definitions:  df-bi 114  df-ral 2328
This theorem is referenced by:  reximia  2431  rmoimia  2764  iuneq2i  3703  iineq2i  3704  dfiun2  3719  dfiin2  3720  dfiun3  4619  dfiin3  4620  cnviinm  4887  bj-omtrans  10468
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