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Theorem mprg 2527
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 2523 . 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 2141  wral 2448
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 1442
This theorem depends on definitions:  df-bi 116  df-ral 2453
This theorem is referenced by:  reximia  2565  rmoimia  2932  iuneq2i  3891  iineq2i  3892  dfiun2  3907  dfiin2  3908  dfiun3  4870  dfiin3  4871  cnviinm  5152  ixpintm  6703  sumeq2i  11327  prodeq2i  11525  2sqlem1  13744  bj-omtrans  13991
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