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Theorem ex-un 21732
 Description: Example for df-un 3325. Example by David A. Wheeler. (Contributed by Mario Carneiro, 6-May-2015.)
Assertion
Ref Expression
ex-un

Proof of Theorem ex-un
StepHypRef Expression
1 unass 3504 . . 3
2 snsspr1 3947 . . . . 5
3 ssequn2 3520 . . . . 5
42, 3mpbi 200 . . . 4
54uneq1i 3497 . . 3
61, 5eqtr3i 2458 . 2
7 df-pr 3821 . . 3
87uneq2i 3498 . 2
9 df-tp 3822 . 2
106, 8, 93eqtr4i 2466 1
 Colors of variables: wff set class Syntax hints:   wceq 1652   cun 3318   wss 3320  csn 3814  cpr 3815  ctp 3816  c1 8991  c3 10050  c8 10055 This theorem is referenced by:  ex-uni  21734 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 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-v 2958  df-un 3325  df-in 3327  df-ss 3334  df-pr 3821  df-tp 3822
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