ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  mpgbi GIF version

Theorem mpgbi 1429
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 1426 . 2 𝑥𝜑
3 mpgbi.1 . 2 (∀𝑥𝜑𝜓)
42, 3mpbi 144 1 𝜓
Colors of variables: wff set class
Syntax hints:  wb 104  wal 1330
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-gen 1426
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  nex  1477  exlimih  1573  exan  1672  abbii  2256  bj-ex  13138
  Copyright terms: Public domain W3C validator