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Theorem mpgbi 1357
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 1354 . 2 𝑥𝜑
3 mpgbi.1 . 2 (∀𝑥𝜑𝜓)
42, 3mpbi 137 1 𝜓
Colors of variables: wff set class
Syntax hints:  wb 102  wal 1257
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-gen 1354
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  nex  1405  exlimih  1500  exan  1599  abbii  2169  bj-ex  10289
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