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Theorem reuxfr4d 23930
 Description: Transfer existential uniqueness from a variable to another variable contained in expression . Cf. reuxfrd 4707 (Contributed by Thierry Arnoux, 7-Apr-2017.)
Hypotheses
Ref Expression
reuxfr4d.1
reuxfr4d.2
reuxfr4d.3
Assertion
Ref Expression
reuxfr4d
Distinct variable groups:   ,,   ,   ,   ,   ,,   ,,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem reuxfr4d
StepHypRef Expression
1 reuxfr4d.2 . . . . . 6
2 reurex 2882 . . . . . 6
31, 2syl 16 . . . . 5
43biantrurd 495 . . . 4
5 r19.41v 2821 . . . . . 6
6 reuxfr4d.3 . . . . . . . 8
76pm5.32da 623 . . . . . . 7
87rexbidv 2687 . . . . . 6
95, 8syl5bbr 251 . . . . 5
109adantr 452 . . . 4
114, 10bitrd 245 . . 3
1211reubidva 2851 . 2
13 reuxfr4d.1 . . 3
14 reurmo 2883 . . . 4
151, 14syl 16 . . 3
1613, 15reuxfr3d 23929 . 2
1712, 16bitrd 245 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1649   wcel 1721  wrex 2667  wreu 2668  wrmo 2669 This theorem is referenced by:  rmoxfrdOLD  23932  rmoxfrd  23933 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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