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Theorem unisn2 4589
 Description: A version of unisn 4266 without the hypothesis. (Contributed by Stefan Allan, 14-Mar-2006.)
Assertion
Ref Expression
unisn2

Proof of Theorem unisn2
StepHypRef Expression
1 unisng 4267 . . 3
2 prid2g 4140 . . 3
31, 2eqeltrd 2555 . 2
4 snprc 4097 . . . . 5
54biimpi 194 . . . 4
65unieqd 4261 . . 3
7 uni0 4278 . . . 4
8 0ex 4583 . . . . 5
98prid1 4141 . . . 4
107, 9eqeltri 2551 . . 3
116, 10syl6eqel 2563 . 2
123, 11pm2.61i 164 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wceq 1379   wcel 1767  cvv 3118  c0 3790  csn 4033  cpr 4035  cuni 4251 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-nul 4582 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2822  df-rex 2823  df-v 3120  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-nul 3791  df-sn 4034  df-pr 4036  df-uni 4252 This theorem is referenced by: (None)
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