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Theorem ex-un 25953
 Description: Example for df-un 3395. 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 3582 . . 3
2 snsspr1 4112 . . . . 5
3 ssequn2 3598 . . . . 5
42, 3mpbi 213 . . . 4
54uneq1i 3575 . . 3
61, 5eqtr3i 2495 . 2
7 df-pr 3962 . . 3
87uneq2i 3576 . 2
9 df-tp 3964 . 2
106, 8, 93eqtr4i 2503 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1452   cun 3388   wss 3390  csn 3959  cpr 3961  ctp 3963  c1 9558  c3 10682  c8 10687 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-v 3033  df-un 3395  df-in 3397  df-ss 3404  df-pr 3962  df-tp 3964 This theorem is referenced by:  ex-uni  25955
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