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Theorem mpgbi 1559
Description: Modus ponens on biconditional combined with generalization. (Contributed by NM, 24-May-1994.) (Proof shortened by Stefan Allan, 28-Oct-2008.)
Hypotheses
Ref Expression
mpgbi.1  |-  ( A. x ph  <->  ps )
mpgbi.2  |-  ph
Assertion
Ref Expression
mpgbi  |-  ps

Proof of Theorem mpgbi
StepHypRef Expression
1 mpgbi.2 . . 3  |-  ph
21ax-gen 1556 . 2  |-  A. x ph
3 mpgbi.1 . 2  |-  ( A. x ph  <->  ps )
42, 3mpbi 201 1  |-  ps
Colors of variables: wff set class
Syntax hints:    <-> wb 178   A.wal 1550
This theorem is referenced by:  nex  1565  exlimi  1822  exlimihOLD  1824  exanOLD  1905  axi12  2417  abbii  2550  nalset  4342  bnj1304  29253  bnj1052  29406  bnj1030  29418
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556
This theorem depends on definitions:  df-bi 179
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