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Theorem 2eu7 2385
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 1840 . . . 4
21nfeu 2300 . . 3
32euan 2351 . 2
4 ancom 450 . . . . 5
54eubii 2306 . . . 4
6 nfe1 1840 . . . . 5
76euan 2351 . . . 4
8 ancom 450 . . . 4
95, 7, 83bitri 271 . . 3
109eubii 2306 . 2
11 ancom 450 . 2
123, 10, 113bitr4ri 278 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  E.wex 1612  E!weu 2282
This theorem is referenced by:  2eu8  2386
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-eu 2286
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