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Theorem 2reu7 28072
 Description: Two equivalent expressions for double restricted existential uniqueness, analogous to 2eu7 2242. (Contributed by Alexander van der Vekens, 2-Jul-2017.)
Assertion
Ref Expression
2reu7
Distinct variable groups:   ,   ,,
Allowed substitution hints:   (,)   ()

Proof of Theorem 2reu7
StepHypRef Expression
1 nfcv 2432 . . . 4
2 nfre1 2612 . . . 4
31, 2nfreu 2727 . . 3
43reuan 28061 . 2
5 ancom 437 . . . . 5
65reubii 2739 . . . 4
7 nfre1 2612 . . . . 5
87reuan 28061 . . . 4
9 ancom 437 . . . 4
106, 8, 93bitri 262 . . 3
1110reubii 2739 . 2
12 ancom 437 . 2
134, 11, 123bitr4ri 269 1
 Colors of variables: wff set class Syntax hints:   wb 176   wa 358  wrex 2557  wreu 2558 This theorem is referenced by:  2reu8  28073 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-reu 2563  df-rmo 2564
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