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Theorem rspct 3203
 Description: A closed version of rspc 3204. (Contributed by Andrew Salmon, 6-Jun-2011.)
Hypothesis
Ref Expression
rspct.1
Assertion
Ref Expression
rspct
Distinct variable groups:   ,   ,

Proof of Theorem rspct
StepHypRef Expression
1 df-ral 2812 . . . 4
2 eleq1 2529 . . . . . . . . . 10
32adantr 465 . . . . . . . . 9
4 simpr 461 . . . . . . . . 9
53, 4imbi12d 320 . . . . . . . 8
65ex 434 . . . . . . 7
76a2i 13 . . . . . 6
87alimi 1633 . . . . 5
9 nfv 1707 . . . . . . 7
10 rspct.1 . . . . . . 7
119, 10nfim 1920 . . . . . 6
12 nfcv 2619 . . . . . 6
1311, 12spcgft 3186 . . . . 5
148, 13syl 16 . . . 4
151, 14syl7bi 230 . . 3
1615com34 83 . 2
1716pm2.43d 48 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  F/wnf 1616  e.wcel 1818  A.wral 2807 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-v 3111
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