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Theorem unisn2 4711
 Description: A version of unisn 4031 without the hypothesis. (Contributed by Stefan Allan, 14-Mar-2006.)
Assertion
Ref Expression
unisn2

Proof of Theorem unisn2
StepHypRef Expression
1 unisng 4032 . . 3
2 prid2g 3911 . . 3
31, 2eqeltrd 2510 . 2
4 snprc 3871 . . . . 5
54biimpi 187 . . . 4
65unieqd 4026 . . 3
7 uni0 4042 . . . 4
8 0ex 4339 . . . . 5
98prid1 3912 . . . 4
107, 9eqeltri 2506 . . 3
116, 10syl6eqel 2524 . 2
123, 11pm2.61i 158 1
 Colors of variables: wff set class Syntax hints:   wn 3   wceq 1652   wcel 1725  cvv 2956  c0 3628  csn 3814  cpr 3815  cuni 4015 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  ax-ext 2417  ax-nul 4338 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-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-sn 3820  df-pr 3821  df-uni 4016
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