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Theorem 2reu2 28053
 Description: Double restricted existential uniqueness, analogous to 2eu2 2369. (Contributed by Alexander van der Vekens, 29-Jun-2017.)
Assertion
Ref Expression
2reu2
Distinct variable groups:   ,,   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem 2reu2
StepHypRef Expression
1 reurmo 2932 . . 3
2 2rmorex 3147 . . 3
3 2reu1 28052 . . . 4
4 simpl 445 . . . 4
53, 4syl6bi 221 . . 3
61, 2, 53syl 19 . 2
7 2rexreu 28051 . . 3
87expcom 426 . 2
96, 8impbid 185 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wral 2712  wrex 2713  wreu 2714  wrmo 2715 This theorem is referenced by:  2reu8  28058 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424 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 1661  df-eu 2292  df-mo 2293  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ral 2717  df-rex 2718  df-reu 2719  df-rmo 2720
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