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Theorem mprg 2378
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 2374 . 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 1393   A.wral 2306
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-gen 1338
This theorem depends on definitions:  df-bi 110  df-ral 2311
This theorem is referenced by:  reximia  2414  rmoimia  2741  iuneq2i  3675  iineq2i  3676  dfiun2  3691  dfiin2  3692  dfiun3  4591  dfiin3  4592  cnviinm  4859  bj-omtrans  10081
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