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Mirrors > Home > NFE Home > Th. List > nceq | Unicode version |
Description: Cardinality equality law. (Contributed by SF, 24-Feb-2015.) |
Ref | Expression |
---|---|
nceq | Nc Nc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eceq1 5962 | . 2 | |
2 | df-nc 6101 | . 2 Nc | |
3 | df-nc 6101 | . 2 Nc | |
4 | 1, 2, 3 | 3eqtr4g 2410 | 1 Nc Nc |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1642 cec 5945 cen 6028 Nc cnc 6091 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 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-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-rex 2620 df-sn 3741 df-ima 4727 df-ec 5947 df-nc 6101 |
This theorem is referenced by: nceqi 6109 nceqd 6110 ncelncs 6120 1cnc 6139 ncaddccl 6144 ce0addcnnul 6179 nc0le1 6216 ce0lenc1 6239 muc0or 6252 |
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