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Theorem mpgbi 1622
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 1619 . 2  |-  A. x ph
3 mpgbi.1 . 2  |-  ( A. x ph  <->  ps )
42, 3mpbi 208 1  |-  ps
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184   A.wal 1393
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619
This theorem depends on definitions:  df-bi 185
This theorem is referenced by:  nex  1628  exlimi  1913  axi12  2433  abbii  2591  nalset  4593  bnj1304  34064  bnj1052  34217  bnj1030  34229  bj-abbii  34549  bj-nalset  34566  bj-nuliota  34772
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