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Theorem eusv2nf 4569
 Description: Two ways to express single-valuedness of a class expression . (Contributed by Mario Carneiro, 18-Nov-2016.)
Hypothesis
Ref Expression
eusv2.1
Assertion
Ref Expression
eusv2nf
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem eusv2nf
StepHypRef Expression
1 nfeu1 2186 . . . 4
2 nfe1 1723 . . . . . . 7
32nfeu 2192 . . . . . 6
4 eusv2.1 . . . . . . . . 9
54isseti 2828 . . . . . . . 8
6 19.8a 1739 . . . . . . . . . 10
76ancri 535 . . . . . . . . 9
87eximi 1567 . . . . . . . 8
95, 8ax-mp 8 . . . . . . 7
10 eupick 2239 . . . . . . 7
119, 10mpan2 652 . . . . . 6
123, 11alrimi 1769 . . . . 5
13 nf3 1830 . . . . 5
1412, 13sylibr 203 . . . 4
151, 14alrimi 1769 . . 3
16 dfnfc2 3882 . . . 4
1716, 4mpg 1539 . . 3
1815, 17sylibr 203 . 2
19 eusvnfb 4567 . . . 4
204, 19mpbiran2 885 . . 3
21 eusv2i 4568 . . 3
2220, 21sylbir 204 . 2
2318, 22impbii 180 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wal 1531  wex 1532  wnf 1535   wceq 1633   wcel 1701  weu 2176  wnfc 2439  cvv 2822 This theorem is referenced by:  eusv2  4570 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897  ax-ext 2297 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1533  df-nf 1536  df-sb 1640  df-eu 2180  df-mo 2181  df-clab 2303  df-cleq 2309  df-clel 2312  df-nfc 2441  df-ral 2582  df-rex 2583  df-v 2824  df-sbc 3026  df-csb 3116  df-un 3191  df-sn 3680  df-pr 3681  df-uni 3865
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