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Theorem rspct 3118
 Description: A closed version of rspc 3119. (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 2719 . . . 4
2 eleq1 2494 . . . . . . . . . 10
32adantr 466 . . . . . . . . 9
4 simpr 462 . . . . . . . . 9
53, 4imbi12d 321 . . . . . . . 8
65ex 435 . . . . . . 7
76a2i 14 . . . . . 6
87alimi 1678 . . . . 5
9 nfv 1755 . . . . . . 7
10 rspct.1 . . . . . . 7
119, 10nfim 1980 . . . . . 6
12 nfcv 2569 . . . . . 6
1311, 12spcgft 3101 . . . . 5
148, 13syl 17 . . . 4
151, 14syl7bi 233 . . 3
1615com34 86 . 2
1716pm2.43d 50 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370  wal 1435   wceq 1437  wnf 1661   wcel 1872  wral 2714 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2063  ax-ext 2408 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2558  df-ral 2719  df-v 3024 This theorem is referenced by: (None)
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