MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  reuxfr2d Unicode version

Theorem reuxfr2d 4675
Description: Transfer existential uniqueness from a variable to another variable contained in expression . (Contributed by NM, 16-Jan-2012.) (Revised by NM, 16-Jun-2017.)
Hypotheses
Ref Expression
reuxfr2d.1
reuxfr2d.2
Assertion
Ref Expression
reuxfr2d
Distinct variable groups:   , ,   ,   ,   , ,

Proof of Theorem reuxfr2d
StepHypRef Expression
1 reuxfr2d.2 . . . . . . 7
2 rmoan 3298 . . . . . . 7
31, 2syl 16 . . . . . 6
4 ancom 450 . . . . . . 7
54rmobii 3049 . . . . . 6
63, 5sylib 196 . . . . 5
76ralrimiva 2871 . . . 4
8 2reuswap 3302 . . . 4
97, 8syl 16 . . 3
10 df-rmo 2815 . . . . . 6
1110ralbii 2888 . . . . 5
12 2reuswap 3302 . . . . 5
1311, 12sylbir 213 . . . 4
14 moeq 3275 . . . . . . 7
1514moani 2346 . . . . . 6
16 ancom 450 . . . . . . . 8
17 an12 797 . . . . . . . 8
1816, 17bitri 249 . . . . . . 7
1918mobii 2307 . . . . . 6
2015, 19mpbi 208 . . . . 5
2120a1i 11 . . . 4
2213, 21mprg 2820 . . 3
239, 22impbid1 203 . 2
24 reuxfr2d.1 . . . 4
25 biidd 237 . . . . 5
2625ceqsrexv 3233 . . . 4
2724, 26syl 16 . . 3
2827reubidva 3041 . 2
2923, 28bitrd 253 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  E*wmo 2283  A.wral 2807  E.wrex 2808  E!wreu 2809  E*wrmo 2810
This theorem is referenced by:  reuxfr2  4676  reuxfrd  4677
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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-ral 2812  df-rex 2813  df-reu 2814  df-rmo 2815  df-v 3111
  Copyright terms: Public domain W3C validator