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Theorem mpgbi 1723
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 1720 . 2 𝑥𝜑
3 mpgbi.1 . 2 (∀𝑥𝜑𝜓)
42, 3mpbi 220 1 𝜓
Colors of variables: wff setvar class
Syntax hints:  wb 196  wal 1479
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720
This theorem depends on definitions:  df-bi 197
This theorem is referenced by:  nex  1729  exlimi  2084  exlimiOLD  2219  axi12  2598  abbii  2737  nalset  4786  bnj1304  30864  bnj1052  31017  bnj1030  31029  bj-abbii  32752  bj-nalset  32769  bj-nuliota  32994  spr0nelg  41491
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