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Theorem mprg 2464
Description: Modus ponens combined with restricted generalization. (Contributed by NM, 10-Aug-2004.)
Hypotheses
Ref Expression
mprg.1 (∀𝑥𝐴 𝜑𝜓)
mprg.2 (𝑥𝐴𝜑)
Assertion
Ref Expression
mprg 𝜓

Proof of Theorem mprg
StepHypRef Expression
1 mprg.2 . . 3 (𝑥𝐴𝜑)
21rgen 2460 . 2 𝑥𝐴 𝜑
3 mprg.1 . 2 (∀𝑥𝐴 𝜑𝜓)
42, 3ax-mp 5 1 𝜓
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1463  wral 2391
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1408
This theorem depends on definitions:  df-bi 116  df-ral 2396
This theorem is referenced by:  reximia  2502  rmoimia  2857  iuneq2i  3799  iineq2i  3800  dfiun2  3815  dfiin2  3816  dfiun3  4766  dfiin3  4767  cnviinm  5048  ixpintm  6585  sumeq2i  11073  bj-omtrans  12956
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