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Theorem ralxpf 5019
 Description: Version of ralxp 5016 with bound-variable hypotheses. (Contributed by NM, 18-Aug-2006.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
ralxpf.1
ralxpf.2
ralxpf.3
ralxpf.4
Assertion
Ref Expression
ralxpf
Distinct variable groups:   ,,   ,,,
Allowed substitution hints:   (,,)   (,,)   ()

Proof of Theorem ralxpf
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 cbvralsv 2943 . 2
2 cbvralsv 2943 . . . 4
32ralbii 2729 . . 3
4 nfv 1629 . . . 4
5 nfcv 2572 . . . . 5
6 nfs1v 2182 . . . . 5
75, 6nfral 2759 . . . 4
8 sbequ12 1944 . . . . 5
98ralbidv 2725 . . . 4
104, 7, 9cbvral 2928 . . 3
11 vex 2959 . . . . . 6
12 vex 2959 . . . . . 6
1311, 12eqvinop 4441 . . . . 5
14 ralxpf.1 . . . . . . . 8
1514nfsb 2185 . . . . . . 7
166nfsb 2185 . . . . . . 7
1715, 16nfbi 1856 . . . . . 6
18 ralxpf.2 . . . . . . . . 9
1918nfsb 2185 . . . . . . . 8
20 nfs1v 2182 . . . . . . . 8
2119, 20nfbi 1856 . . . . . . 7
22 ralxpf.3 . . . . . . . . 9
23 ralxpf.4 . . . . . . . . 9
2422, 23sbhypf 3001 . . . . . . . 8
25 vex 2959 . . . . . . . . . 10
26 vex 2959 . . . . . . . . . 10
2725, 26opth 4435 . . . . . . . . 9
28 sbequ12 1944 . . . . . . . . . 10
298, 28sylan9bb 681 . . . . . . . . 9
3027, 29sylbi 188 . . . . . . . 8
3124, 30sylan9bb 681 . . . . . . 7
3221, 31exlimi 1821 . . . . . 6
3317, 32exlimi 1821 . . . . 5
3413, 33sylbi 188 . . . 4
3534ralxp 5016 . . 3
363, 10, 353bitr4ri 270 . 2
371, 36bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550  wnf 1553   wceq 1652  wsb 1658  wral 2705  cop 3817   cxp 4876 This theorem is referenced by:  rexxpf  5020 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-iun 4095  df-opab 4267  df-xp 4884  df-rel 4885
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