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Theorem mprg 2534
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 2530 . 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 2148  wral 2455
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-gen 1449
This theorem depends on definitions:  df-bi 117  df-ral 2460
This theorem is referenced by:  reximia  2572  rmoimia  2941  iuneq2i  3906  iineq2i  3907  dfiun2  3922  dfiin2  3923  dfiun3  4888  dfiin3  4889  cnviinm  5172  ixpintm  6727  sumeq2i  11374  prodeq2i  11572  2sqlem1  14546  bj-omtrans  14793
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