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Mirrors > Home > ILE Home > Th. List > moeq | Unicode version |
Description: There is at most one set equal to a class. (Contributed by NM, 8-Mar-1995.) |
Ref | Expression |
---|---|
moeq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isset 2718 | . . . 4 | |
2 | eueq 2883 | . . . 4 | |
3 | 1, 2 | bitr3i 185 | . . 3 |
4 | 3 | biimpi 119 | . 2 |
5 | df-mo 2010 | . 2 | |
6 | 4, 5 | mpbir 145 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1335 wex 1472 weu 2006 wmo 2007 wcel 2128 cvv 2712 |
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-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-v 2714 |
This theorem is referenced by: euxfr2dc 2897 reueq 2911 mosn 3595 sndisj 3961 disjxsn 3963 reusv1 4418 funopabeq 5206 funcnvsn 5215 fvmptg 5544 fvopab6 5564 ovmpt4g 5943 ovi3 5957 ov6g 5958 oprabex3 6077 1stconst 6168 2ndconst 6169 axaddf 7788 axmulf 7789 |
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