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Theorem mpgbi 1672
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 1669 . 2  |-  A. x ph
3 mpgbi.1 . 2  |-  ( A. x ph  <->  ps )
42, 3mpbi 212 1  |-  ps
Colors of variables: wff setvar class
Syntax hints:    <-> wb 188   A.wal 1442
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669
This theorem depends on definitions:  df-bi 189
This theorem is referenced by:  nex  1678  exlimi  1995  axi12  2429  abbii  2567  nalset  4540  bnj1304  29631  bnj1052  29784  bnj1030  29796  bj-abbii  31392  bj-nalset  31409  bj-nuliota  31623
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