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

Theorem mprg 2514
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 2510 . 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 2128   A.wral 2435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1429
This theorem depends on definitions:  df-bi 116  df-ral 2440
This theorem is referenced by:  reximia  2552  rmoimia  2914  iuneq2i  3869  iineq2i  3870  dfiun2  3885  dfiin2  3886  dfiun3  4847  dfiin3  4848  cnviinm  5129  ixpintm  6672  sumeq2i  11272  prodeq2i  11470  bj-omtrans  13602
  Copyright terms: Public domain W3C validator