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Theorem rspc2 2683
 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 2194 . . . 4
2 rspc2.1 . . . 4
31, 2nfralxy 2377 . . 3
4 rspc2.3 . . . 4
54ralbidv 2343 . . 3
63, 5rspc 2667 . 2
7 rspc2.2 . . 3
8 rspc2.4 . . 3
97, 8rspc 2667 . 2
106, 9sylan9 395 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wb 102   wceq 1259  wnf 1365   wcel 1409  wral 2323 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-v 2576 This theorem is referenced by:  rspc2v  2685
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