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Mirrors > Home > NFE Home > Th. List > reiota2 | Unicode version |
Description: A condition allowing us to represent "the unique element in such that " with a class expression . (Contributed by Scott Fenton, 7-Jan-2018.) |
Ref | Expression |
---|---|
reiota2.1 |
Ref | Expression |
---|---|
reiota2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 443 | . . 3 | |
2 | 1 | biantrurd 494 | . 2 |
3 | df-reu 2621 | . . 3 | |
4 | eleq1 2413 | . . . . 5 | |
5 | reiota2.1 | . . . . 5 | |
6 | 4, 5 | anbi12d 691 | . . . 4 |
7 | 6 | iota2 4367 | . . 3 |
8 | 3, 7 | sylan2b 461 | . 2 |
9 | 2, 8 | bitrd 244 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wceq 1642 wcel 1710 weu 2204 wreu 2616 cio 4337 |
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-or 359 df-an 360 df-3an 936 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ral 2619 df-rex 2620 df-reu 2621 df-v 2861 df-sbc 3047 df-nin 3211 df-compl 3212 df-un 3214 df-sn 3741 df-pr 3742 df-uni 3892 df-iota 4339 |
This theorem is referenced by: ncfinprop 4474 tfinprop 4489 eqtc 6161 |
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