Theorem rexiunxp 5148

Description: Write a double restricted quantification as one universal quantifier. In this version of rexxp 5150, () is not assumed to be constant. (Contributed by Mario Carneiro, 14-Feb-2015.)

Hypothesis

Ref	Expression
ralxp.1

Assertion

Ref	Expression
rexiunxp

Distinct variable groups:   ,,,   ,,   ,,   ,

Proof of Theorem rexiunxp

Step	Hyp	Ref	Expression
1		ralxp.1	. . . . . 6
2	1	notbid 294	. . . . 5
3	2	raliunxp 5147	. . . 4
4		ralnex 2903	. . . . 5
5	4	ralbii 2888	. . . 4
6	3, 5	bitri 249	. . 3
7	6	notbii 296	. 2
8		dfrex2 2908	. 2
9		dfrex2 2908	. 2
10	7, 8, 9	3bitr4i 277	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  =wceq 1395  A.wral 2807  E.wrex 2808  {csn 4029  <.cop 4035  U_ciun 4330  X.cxp 5002

This theorem is referenced by:  rexxp  5150  fsumvma  23488  cvmliftlem15  28743  filnetlem4  30199

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