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Theorem ralxpf 5154
 Description: Version of ralxp 5149 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:   ,,   ,,,

Proof of Theorem ralxpf
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 cbvralsv 3095 . 2
2 cbvralsv 3095 . . . 4
32ralbii 2888 . . 3
4 nfv 1707 . . . 4
5 nfcv 2619 . . . . 5
6 nfs1v 2181 . . . . 5
75, 6nfral 2843 . . . 4
8 sbequ12 1992 . . . . 5
98ralbidv 2896 . . . 4
104, 7, 9cbvral 3080 . . 3
11 vex 3112 . . . . . 6
12 vex 3112 . . . . . 6
1311, 12eqvinop 4736 . . . . 5
14 ralxpf.1 . . . . . . . 8
1514nfsb 2184 . . . . . . 7
166nfsb 2184 . . . . . . 7
1715, 16nfbi 1934 . . . . . 6
18 ralxpf.2 . . . . . . . . 9
1918nfsb 2184 . . . . . . . 8
20 nfs1v 2181 . . . . . . . 8
2119, 20nfbi 1934 . . . . . . 7
22 ralxpf.3 . . . . . . . . 9
23 ralxpf.4 . . . . . . . . 9
2422, 23sbhypf 3156 . . . . . . . 8
25 vex 3112 . . . . . . . . . 10
26 vex 3112 . . . . . . . . . 10
2725, 26opth 4726 . . . . . . . . 9
28 sbequ12 1992 . . . . . . . . . 10
298, 28sylan9bb 699 . . . . . . . . 9
3027, 29sylbi 195 . . . . . . . 8
3124, 30sylan9bb 699 . . . . . . 7
3221, 31exlimi 1912 . . . . . 6
3317, 32exlimi 1912 . . . . 5
3413, 33sylbi 195 . . . 4
3534ralxp 5149 . . 3
363, 10, 353bitr4ri 278 . 2
371, 36bitri 249 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  F/wnf 1616  [wsb 1739  A.wral 2807  <.cop 4035  X.cxp 5002 This theorem is referenced by:  rexxpf  5155 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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  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-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-iun 4332  df-opab 4511  df-xp 5010  df-rel 5011
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