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Theorem rspct 2948
 Description: A closed version of rspc 2949. (Contributed by Andrew Salmon, 6-Jun-2011.)
Hypothesis
Ref Expression
rspct.1
Assertion
Ref Expression
rspct
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rspct
StepHypRef Expression
1 df-ral 2619 . . . 4
2 eleq1 2413 . . . . . . . . . 10
32adantr 451 . . . . . . . . 9
4 simpr 447 . . . . . . . . 9
53, 4imbi12d 311 . . . . . . . 8
65ex 423 . . . . . . 7
76a2i 12 . . . . . 6
87alimi 1559 . . . . 5
9 nfv 1619 . . . . . . 7
10 rspct.1 . . . . . . 7
119, 10nfim 1813 . . . . . 6
12 nfcv 2489 . . . . . 6
1311, 12spcgft 2931 . . . . 5
148, 13syl 15 . . . 4
151, 14syl7bi 221 . . 3
1615com34 77 . 2
1716pm2.43d 44 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wal 1540  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: (None)
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