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Theorem mprg 2372
Description: Modus ponens combined with restricted generalization. (Contributed by NM, 10-Aug-2004.)
Hypotheses
Ref Expression
mprg.1 (x A φψ)
mprg.2 (x Aφ)
Assertion
Ref Expression
mprg ψ

Proof of Theorem mprg
StepHypRef Expression
1 mprg.2 . . 3 (x Aφ)
21rgen 2368 . 2 x A φ
3 mprg.1 . 2 (x A φψ)
42, 3ax-mp 7 1 ψ
Colors of variables: wff set class
Syntax hints:  wi 4   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:  reximia  2408  rmoimia  2735  iuneq2i  3666  iineq2i  3667  dfiun2  3682  dfiin2  3683  dfiun3  4534  dfiin3  4535  cnviinm  4802  bj-omtrans  9344
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