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Mirrors > Home > NFE Home > Th. List > iuneq2 | Unicode version |
Description: Equality theorem for indexed union. (Contributed by NM, 22-Oct-2003.) |
Ref | Expression |
---|---|
iuneq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ss2iun 3984 | . . 3 | |
2 | ss2iun 3984 | . . 3 | |
3 | 1, 2 | anim12i 549 | . 2 |
4 | eqss 3287 | . . . 4 | |
5 | 4 | ralbii 2638 | . . 3 |
6 | r19.26 2746 | . . 3 | |
7 | 5, 6 | bitri 240 | . 2 |
8 | eqss 3287 | . 2 | |
9 | 3, 7, 8 | 3imtr4i 257 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 358 wceq 1642 wral 2614 wss 3257 ciun 3969 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 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-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ral 2619 df-rex 2620 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-ss 3259 df-iun 3971 |
This theorem is referenced by: iuneq2i 3987 iuneq2dv 3990 |
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