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Theorem mprg 2421
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 2417 . 2 𝑥𝐴 𝜑
3 mprg.1 . 2 (∀𝑥𝐴 𝜑𝜓)
42, 3ax-mp 7 1 𝜓
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1434  wral 2349
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-gen 1379
This theorem depends on definitions:  df-bi 115  df-ral 2354
This theorem is referenced by:  reximia  2457  rmoimia  2793  iuneq2i  3704  iineq2i  3705  dfiun2  3720  dfiin2  3721  dfiun3  4619  dfiin3  4620  cnviinm  4889  bj-omtrans  10936
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