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Theorem ex-pw 25958
 Description: Example for df-pw 3944. Example by David A. Wheeler. (Contributed by Mario Carneiro, 2-Jul-2016.)
Assertion
Ref Expression
ex-pw

Proof of Theorem ex-pw
StepHypRef Expression
1 pweq 3945 . 2
2 qdass 4062 . . . 4
3 qdassr 4063 . . . 4
42, 3uneq12i 3577 . . 3
5 pwtp 4187 . . 3
6 df-tp 3964 . . . . . . . 8
76uneq2i 3576 . . . . . . 7
8 unass 3582 . . . . . . 7
97, 8eqtr4i 2496 . . . . . 6
10 tpass 4061 . . . . . . 7
1110uneq1i 3575 . . . . . 6
129, 11eqtr4i 2496 . . . . 5
13 unass 3582 . . . . . 6
14 tpass 4061 . . . . . . 7
1514uneq1i 3575 . . . . . 6
16 df-tp 3964 . . . . . . 7
1716uneq2i 3576 . . . . . 6
1813, 15, 173eqtr4i 2503 . . . . 5
1912, 18uneq12i 3577 . . . 4
20 un4 3585 . . . 4
2119, 20eqtr4i 2496 . . 3
224, 5, 213eqtr4i 2503 . 2
231, 22syl6eq 2521 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1452   cun 3388  c0 3722  cpw 3942  csn 3959  cpr 3961  ctp 3963  c3 10682  c5 10684  c7 10686 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-3or 1008  df-3an 1009  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-ral 2761  df-v 3033  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-pw 3944  df-sn 3960  df-pr 3962  df-tp 3964 This theorem is referenced by: (None)
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