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Mirrors > Home > NFE Home > Th. List > 0iin | Unicode version |
Description: An empty indexed intersection is the universal class. (Contributed by NM, 20-Oct-2005.) |
Ref | Expression |
---|---|
0iin |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-iin 3972 | . 2 | |
2 | vex 2862 | . . . 4 | |
3 | ral0 3654 | . . . 4 | |
4 | 2, 3 | 2th 230 | . . 3 |
5 | 4 | abbi2i 2464 | . 2 |
6 | 1, 5 | eqtr4i 2376 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1642 wcel 1710 cab 2339 wral 2614 cvv 2859 c0 3550 ciin 3970 |
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-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-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-dif 3215 df-nul 3551 df-iin 3972 |
This theorem is referenced by: iinrab2 4029 riin0 4039 |
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