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Mirrors > Home > ILE Home > Th. List > eqvisset | Unicode version |
Description: A class equal to a variable is a set. Note the absence of disjoint variable condition, contrary to isset 2718 and issetri 2721. (Contributed by BJ, 27-Apr-2019.) |
Ref | Expression |
---|---|
eqvisset |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2715 | . 2 | |
2 | eleq1 2220 | . 2 | |
3 | 1, 2 | mpbii 147 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1335 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-5 1427 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-v 2714 |
This theorem is referenced by: elxp5 5074 xpsnen 6766 fival 6914 |
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