indifundif - Mathbox for Thierry Arnoux

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Theorem indifundif 29356

Description: A remarkable equation with sets. (Contributed by Thierry Arnoux, 18-May-2020.)

**Assertion**
Ref	Expression
indifundif	$\$ $\$ $\$

**Proof of Theorem indifundif**
Step	Hyp	Ref	Expression
1		difindi 3881	. 2 $\$ $\$ $\$
2		difundir 3880	. . . . 5 $\$ $\$ $\$ $\$ $\$
3		inundif 4046	. . . . . 6 $\$
4	3	difeq1i 3724	. . . . 5 $\$ $\$ $\$
5		uncom 3757	. . . . 5 $\$ $\$ $\$ $\$ $\$ $\$
6	2, 4, 5	3eqtr3i 2652	. . . 4 $\$ $\$ $\$ $\$
7	6	uneq2i 3764	. . 3 $\$ $\$ $\$ $\$ $\$ $\$
8		unass 3770	. . 3 $\$ $\$ $\$ $\$ $\$ $\$ $\$ $\$
9		undifabs 4045	. . . 4 $\$ $\$ $\$ $\$
10	9	uneq1i 3763	. . 3 $\$ $\$ $\$ $\$ $\$ $\$
11	7, 8, 10	3eqtr2i 2650	. 2 $\$ $\$ $\$ $\$
12		uncom 3757	. 2 $\$ $\$ $\$ $\$
13	1, 11, 12	3eqtrri 2649	1 $\$ $\$ $\$

Colors of variables: wff setvar class

Syntax hints:

wceq 1483 $\$ cdif 3571

cun 3572

cin 3573

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602

This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581

This theorem is referenced by: inelcarsg 30373