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Theorem rspc2 3057
 Description: 2-variable restricted specialization, using implicit substitution. (Contributed by NM, 9-Nov-2012.)
Hypotheses
Ref Expression
rspc2.1
rspc2.2
rspc2.3
rspc2.4
Assertion
Ref Expression
rspc2
Distinct variable groups:   ,,   ,   ,   ,,
Allowed substitution hints:   (,)   (,)   (,)   ()   ()

Proof of Theorem rspc2
StepHypRef Expression
1 nfcv 2572 . . . 4
2 rspc2.1 . . . 4
31, 2nfral 2759 . . 3
4 rspc2.3 . . . 4
54ralbidv 2725 . . 3
63, 5rspc 3046 . 2
7 rspc2.2 . . 3
8 rspc2.4 . . 3
97, 8rspc 3046 . 2
106, 9sylan9 639 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wnf 1553   wceq 1652   wcel 1725  wral 2705 This theorem is referenced by:  rspc2v  3058  dvmptfsum  19859  fphpd  26877 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-v 2958
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