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Mirrors > Home > NFE Home > Th. List > elex22 | Unicode version |
Description: If two classes each contain another class, then both contain some set. (Contributed by Alan Sare, 24-Oct-2011.) |
Ref | Expression |
---|---|
elex22 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1a 2422 | . . . 4 | |
2 | eleq1a 2422 | . . . 4 | |
3 | 1, 2 | anim12ii 553 | . . 3 |
4 | 3 | alrimiv 1631 | . 2 |
5 | elisset 2869 | . . 3 | |
6 | 5 | adantr 451 | . 2 |
7 | exim 1575 | . 2 | |
8 | 4, 6, 7 | sylc 56 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 358 wal 1540 wex 1541 wceq 1642 wcel 1710 |
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-11 1746 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-v 2861 |
This theorem is referenced by: (None) |
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