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Theorem 2eu8 2367
 Description: Two equivalent expressions for double existential uniqueness. Curiously, we can put on either of the internal conjuncts but not both. We can also commute using 2eu7 2366. (Contributed by NM, 20-Feb-2005.)
Assertion
Ref Expression
2eu8

Proof of Theorem 2eu8
StepHypRef Expression
1 2eu2 2361 . . 3
21pm5.32i 619 . 2
3 nfeu1 2290 . . . . 5
43nfeu 2296 . . . 4
54euan 2337 . . 3
6 ancom 438 . . . . . 6
76eubii 2289 . . . . 5
8 nfe1 1747 . . . . . 6
98euan 2337 . . . . 5
10 ancom 438 . . . . 5
117, 9, 103bitri 263 . . . 4
1211eubii 2289 . . 3
13 ancom 438 . . 3
145, 12, 133bitr4ri 270 . 2
15 2eu7 2366 . 2
162, 14, 153bitr3ri 268 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359  wex 1550  weu 2280 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285
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