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Theorem eusv2nf 4622
 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 2279 . . . 4
2 nfe1 1894 . . . . . . 7
32nfeu 2285 . . . . . 6
4 eusv2.1 . . . . . . . . 9
54isseti 3086 . . . . . . . 8
6 19.8a 1912 . . . . . . . . 9
76ancri 554 . . . . . . . 8
85, 7eximii 1703 . . . . . . 7
9 eupick 2335 . . . . . . 7
108, 9mpan2 675 . . . . . 6
113, 10alrimi 1932 . . . . 5
12 nf3 2021 . . . . 5
1311, 12sylibr 215 . . . 4
141, 13alrimi 1932 . . 3
15 dfnfc2 4237 . . . 4
1615, 4mpg 1665 . . 3
1714, 16sylibr 215 . 2
18 eusvnfb 4620 . . . 4
194, 18mpbiran2 927 . . 3
20 eusv2i 4621 . . 3
2119, 20sylbir 216 . 2
2217, 21impbii 190 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370  wal 1435   wceq 1437  wex 1657  wnf 1661   wcel 1872  weu 2269  wnfc 2566  cvv 3080 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-fal 1443  df-ex 1658  df-nf 1662  df-sb 1791  df-eu 2273  df-mo 2274  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ral 2776  df-rex 2777  df-v 3082  df-sbc 3300  df-csb 3396  df-dif 3439  df-un 3441  df-in 3443  df-ss 3450  df-nul 3762  df-sn 3999  df-pr 4001  df-uni 4220 This theorem is referenced by:  eusv2  4623
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