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Theorem mpgbi 1873
 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 (∀𝑥𝜑𝜓)
mpgbi.2 𝜑
Assertion
Ref Expression
mpgbi 𝜓

Proof of Theorem mpgbi
StepHypRef Expression
1 mpgbi.2 . . 3 𝜑
21ax-gen 1870 . 2 𝑥𝜑
3 mpgbi.1 . 2 (∀𝑥𝜑𝜓)
42, 3mpbi 220 1 𝜓
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 196  ∀wal 1629 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870 This theorem depends on definitions:  df-bi 197 This theorem is referenced by:  nex  1879  exlimi  2242  exlimiOLD  2383  axi12  2749  abbii  2888  nalset  4929  bnj1304  31228  bnj1052  31381  bnj1030  31393  bj-abbii  33113  bj-nalset  33130  bj-nuliota  33350  spr0nelg  42254
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