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Mirrors > Home > ILE Home > Th. List > ceqsexv | Unicode version |
Description: Elimination of an existential quantifier, using implicit substitution. (Contributed by NM, 2-Mar-1995.) |
Ref | Expression |
---|---|
ceqsexv.1 | |
ceqsexv.2 |
Ref | Expression |
---|---|
ceqsexv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1508 | . 2 | |
2 | ceqsexv.1 | . 2 | |
3 | ceqsexv.2 | . 2 | |
4 | 1, 2, 3 | ceqsex 2719 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wex 1468 wcel 1480 cvv 2681 |
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 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-v 2683 |
This theorem is referenced by: ceqsex3v 2723 gencbvex 2727 sbhypf 2730 euxfr2dc 2864 inuni 4075 eqvinop 4160 onm 4318 uniuni 4367 opeliunxp 4589 elvvv 4597 rexiunxp 4676 imai 4890 coi1 5049 abrexco 5653 opabex3d 6012 opabex3 6013 mapsnen 6698 xpsnen 6708 xpcomco 6713 xpassen 6717 |
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