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Theorem reuxfr2d 4705
 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:   ,,   ,   ,   ,,
Allowed substitution hints:   ()   ()

Proof of Theorem reuxfr2d
StepHypRef Expression
1 reuxfr2d.2 . . . . . . 7
2 rmoan 3092 . . . . . . 7
31, 2syl 16 . . . . . 6
4 ancom 438 . . . . . . 7
54rmobii 2859 . . . . . 6
63, 5sylib 189 . . . . 5
76ralrimiva 2749 . . . 4
8 2reuswap 3096 . . . 4
97, 8syl 16 . . 3
10 df-rmo 2674 . . . . . 6
1110ralbii 2690 . . . . 5
12 2reuswap 3096 . . . . 5
1311, 12sylbir 205 . . . 4
14 moeq 3070 . . . . . . 7
1514moani 2306 . . . . . 6
16 ancom 438 . . . . . . . 8
17 an12 773 . . . . . . . 8
1816, 17bitri 241 . . . . . . 7
1918mobii 2290 . . . . . 6
2015, 19mpbi 200 . . . . 5
2120a1i 11 . . . 4
2213, 21mprg 2735 . . 3
239, 22impbid1 195 . 2
24 reuxfr2d.1 . . . 4
25 biidd 229 . . . . 5
2625ceqsrexv 3029 . . . 4
2724, 26syl 16 . . 3
2827reubidva 2851 . 2
2923, 28bitrd 245 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1649   wcel 1721  wmo 2255  wral 2666  wrex 2667  wreu 2668  wrmo 2669 This theorem is referenced by:  reuxfr2  4706  reuxfrd  4707 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2258  df-mo 2259  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ral 2671  df-rex 2672  df-reu 2673  df-rmo 2674  df-v 2918
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