ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  mprg Unicode version

Theorem mprg 2544
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 2540 . 2  |-  A. x  e.  A  ph
3 mprg.1 . 2  |-  ( A. x  e.  A  ph  ->  ps )
42, 3ax-mp 5 1  |-  ps
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 2158   A.wral 2465
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-gen 1459
This theorem depends on definitions:  df-bi 117  df-ral 2470
This theorem is referenced by:  reximia  2582  rmoimia  2951  iuneq2i  3916  iineq2i  3917  dfiun2  3932  dfiin2  3933  dfiun3  4898  dfiin3  4899  cnviinm  5182  ixpintm  6739  sumeq2i  11386  prodeq2i  11584  2sqlem1  14757  bj-omtrans  15004
  Copyright terms: Public domain W3C validator