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Theorem reuxfrd 4749
 Description: Transfer existential uniqueness from a variable to another variable contained in expression . Use reuhypd 4751 to eliminate the second hypothesis. (Contributed by NM, 16-Jan-2012.)
Hypotheses
Ref Expression
reuxfrd.1
reuxfrd.2
reuxfrd.3
Assertion
Ref Expression
reuxfrd
Distinct variable groups:   ,,   ,   ,   ,   ,,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem reuxfrd
StepHypRef Expression
1 reuxfrd.2 . . . . . 6
2 reurex 2923 . . . . . 6
31, 2syl 16 . . . . 5
43biantrurd 496 . . . 4
5 r19.41v 2862 . . . . 5
6 reuxfrd.3 . . . . . . 7
76pm5.32i 620 . . . . . 6
87rexbii 2731 . . . . 5
95, 8bitr3i 244 . . . 4
104, 9syl6bb 254 . . 3
1110reubidva 2892 . 2
12 reuxfrd.1 . . 3
13 reurmo 2924 . . . 4
141, 13syl 16 . . 3
1512, 14reuxfr2d 4747 . 2
1611, 15bitrd 246 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   wceq 1653   wcel 1726  wrex 2707  wreu 2708  wrmo 2709 This theorem is referenced by:  reuxfr  4750  riotaxfrd  6582 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2286  df-mo 2287  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ral 2711  df-rex 2712  df-reu 2713  df-rmo 2714  df-v 2959
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