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Mirrors > Home > NFE Home > Th. List > qseq2 | Unicode version |
Description: Equality theorem for quotient set. (Contributed by set.mm contributors, 23-Jul-1995.) |
Ref | Expression |
---|---|
qseq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eceq2 5963 | . . . . 5 | |
2 | 1 | eqeq2d 2364 | . . . 4 |
3 | 2 | rexbidv 2635 | . . 3 |
4 | 3 | abbidv 2467 | . 2 |
5 | df-qs 5951 | . 2 | |
6 | df-qs 5951 | . 2 | |
7 | 4, 5, 6 | 3eqtr4g 2410 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1642 cab 2339 wrex 2615 cec 5945 cqs 5946 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-rex 2620 df-br 4640 df-ima 4727 df-ec 5947 df-qs 5951 |
This theorem is referenced by: (None) |
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