Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > clabel | Structured version Visualization version Unicode version |
Description: Membership of a class abstraction in another class. (Contributed by NM, 17-Jan-2006.) |
Ref | Expression |
---|---|
clabel |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-clel 2618 | . 2 | |
2 | abeq2 2732 | . . . 4 | |
3 | 2 | anbi2ci 732 | . . 3 |
4 | 3 | exbii 1774 | . 2 |
5 | 1, 4 | bitri 264 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wal 1481 wceq 1483 wex 1704 wcel 1990 cab 2608 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 |
This theorem is referenced by: sbabel 2793 grothprimlem 9655 ntrneiel2 38384 |
Copyright terms: Public domain | W3C validator |