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Theorem mprgbir 2373
Description: Modus ponens on biconditional combined with restricted generalization. (Contributed by NM, 21-Mar-2004.)
Hypotheses
Ref Expression
mprgbir.1 (φx A ψ)
mprgbir.2 (x Aψ)
Assertion
Ref Expression
mprgbir φ

Proof of Theorem mprgbir
StepHypRef Expression
1 mprgbir.2 . . 3 (x Aψ)
21rgen 2368 . 2 x A ψ
3 mprgbir.1 . 2 (φx A ψ)
42, 3mpbir 134 1 φ
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   wcel 1390  wral 2300
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-gen 1335
This theorem depends on definitions:  df-bi 110  df-ral 2305
This theorem is referenced by:  ss2rabi  3016  rabnc  3244  ssintub  3624  tron  4085  djussxp  4424  dmiin  4523  dfco2  4763  coiun  4773  tfrlem6  5873  oacl  5979  renfdisj  6836  1nn  7666  ioomax  8547  iccmax  8548  bj-omtrans2  9345
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