![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > releq | Structured version Visualization version Unicode version |
Description: Equality theorem for the relation predicate. (Contributed by NM, 1-Aug-1994.) |
Ref | Expression |
---|---|
releq |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseq1 3453 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | df-rel 4841 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | df-rel 4841 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 1, 2, 3 | 3bitr4g 292 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 |
This theorem depends on definitions: df-bi 189 df-an 373 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-clab 2438 df-cleq 2444 df-clel 2447 df-in 3411 df-ss 3418 df-rel 4841 |
This theorem is referenced by: releqi 4918 releqd 4919 dfrel2 5286 tposfn2 6995 ereq1 7370 isps 16448 isdir 16478 fpwrelmapffslem 28317 bnj1321 29836 frrlem6 30523 prtlem12 32439 relintabex 36187 clrellem 36229 clcnvlem 36230 |
Copyright terms: Public domain | W3C validator |