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Theorem 2eu7 2369
 Description: Two equivalent expressions for double existential uniqueness. (Contributed by NM, 19-Feb-2005.)
Assertion
Ref Expression
2eu7

Proof of Theorem 2eu7
StepHypRef Expression
1 nfe1 1748 . . . 4
21nfeu 2299 . . 3
32euan 2340 . 2
4 ancom 439 . . . . 5
54eubii 2292 . . . 4
6 nfe1 1748 . . . . 5
76euan 2340 . . . 4
8 ancom 439 . . . 4
95, 7, 83bitri 264 . . 3
109eubii 2292 . 2
11 ancom 439 . 2
123, 10, 113bitr4ri 271 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360  wex 1551  weu 2283 This theorem is referenced by:  2eu8  2370 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 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951 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 2287  df-mo 2288
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