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Mirrors > Home > NFE Home > Th. List > iinxsng | Unicode version |
Description: A singleton index picks out an instance of an indexed intersection's argument. (Contributed by NM, 15-Jan-2012.) (Proof shortened by Mario Carneiro, 17-Nov-2016.) |
Ref | Expression |
---|---|
iinxsng.1 |
Ref | Expression |
---|---|
iinxsng |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-iin 3972 | . 2 | |
2 | iinxsng.1 | . . . . 5 | |
3 | 2 | eleq2d 2420 | . . . 4 |
4 | 3 | ralsng 3765 | . . 3 |
5 | 4 | abbi1dv 2469 | . 2 |
6 | 1, 5 | syl5eq 2397 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1642 wcel 1710 cab 2339 wral 2614 csn 3737 ciin 3970 |
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-3an 936 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-v 2861 df-sbc 3047 df-sn 3741 df-iin 3972 |
This theorem is referenced by: (None) |
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