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Theorem rspc2 2960
 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 2489 . . . 4
2 rspc2.1 . . . 4
31, 2nfral 2667 . . 3
4 rspc2.3 . . . 4
54ralbidv 2634 . . 3
63, 5rspc 2949 . 2
7 rspc2.2 . . 3
8 rspc2.4 . . 3
97, 8rspc 2949 . 2
106, 9sylan9 638 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wnf 1544   wceq 1642   wcel 1710  wral 2614 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-v 2861 This theorem is referenced by:  rspc2v  2961
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