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Theorem mpgbi 1621
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
mpgbi.2
Assertion
Ref Expression
mpgbi

Proof of Theorem mpgbi
StepHypRef Expression
1 mpgbi.2 . . 3
21ax-gen 1618 . 2
3 mpgbi.1 . 2
42, 3mpbi 208 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  A.wal 1393
This theorem is referenced by:  nex  1627  exlimi  1912  axi12  2433  abbii  2591  nalset  4589  bnj1304  33878  bnj1052  34031  bnj1030  34043  bj-abbii  34363  bj-nalset  34380  bj-nuliota  34586
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618
This theorem depends on definitions:  df-bi 185
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