Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE 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 2209 | . . . 4 | |
2 | eleq1a 2209 | . . . 4 | |
3 | 1, 2 | anim12ii 340 | . . 3 |
4 | 3 | alrimiv 1846 | . 2 |
5 | elisset 2695 | . . 3 | |
6 | 5 | adantr 274 | . 2 |
7 | exim 1578 | . 2 | |
8 | 4, 6, 7 | sylc 62 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1329 wceq 1331 wex 1468 wcel 1480 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-v 2683 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |