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Theorem indifundif 28231
 Description: A remarkable equation with sets. (Contributed by Thierry Arnoux, 18-May-2020.)
Assertion
Ref Expression
indifundif

Proof of Theorem indifundif
StepHypRef Expression
1 difindi 3688 . 2
2 difundir 3687 . . . . 5
3 inundif 3836 . . . . . 6
43difeq1i 3536 . . . . 5
5 uncom 3569 . . . . 5
62, 4, 53eqtr3i 2501 . . . 4
76uneq2i 3576 . . 3
8 unass 3582 . . 3
9 undifabs 3835 . . . 4
109uneq1i 3575 . . 3
117, 8, 103eqtr2i 2499 . 2
12 uncom 3569 . 2
131, 11, 123eqtrri 2498 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1452   cdif 3387   cun 3388   cin 3389 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-ral 2761  df-rab 2765  df-v 3033  df-dif 3393  df-un 3395  df-in 3397 This theorem is referenced by:  inelcarsg  29216
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