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Theorem unisnif 24535
 Description: Express union of singleton in terms of . (Contributed by Scott Fenton, 27-Mar-2014.) (Revised by Mario Carneiro, 19-Apr-2014.)
Assertion
Ref Expression
unisnif

Proof of Theorem unisnif
StepHypRef Expression
1 iftrue 3584 . . . 4
2 unisng 3860 . . . 4
31, 2eqtr4d 2331 . . 3
4 iffalse 3585 . . . 4
5 snprc 3708 . . . . . . 7
65biimpi 186 . . . . . 6
76unieqd 3854 . . . . 5
8 uni0 3870 . . . . 5
97, 8syl6eq 2344 . . . 4
104, 9eqtr4d 2331 . . 3
113, 10pm2.61i 156 . 2
1211eqcomi 2300 1
 Colors of variables: wff set class Syntax hints:   wn 3   wceq 1632   wcel 1696  cvv 2801  c0 3468  cif 3578  csn 3653  cuni 3843 This theorem is referenced by:  dfrdg4  24560 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-uni 3844
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