Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  rspct Structured version   Unicode version

Theorem rspct 3051
 Description: A closed version of rspc 3052. (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 2716 . . . 4
2 eleq1 2502 . . . . . . . . . 10
32adantr 453 . . . . . . . . 9
4 simpr 449 . . . . . . . . 9
53, 4imbi12d 313 . . . . . . . 8
65ex 425 . . . . . . 7
76a2i 13 . . . . . 6
87alimi 1569 . . . . 5
9 nfv 1630 . . . . . . 7
10 rspct.1 . . . . . . 7
119, 10nfim 1834 . . . . . 6
12 nfcv 2578 . . . . . 6
1311, 12spcgft 3034 . . . . 5
148, 13syl 16 . . . 4
151, 14syl7bi 223 . . 3
1615com34 80 . 2
1716pm2.43d 47 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550  wnf 1554   wceq 1653   wcel 1727  wral 2711 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ral 2716  df-v 2964
 Copyright terms: Public domain W3C validator