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Mirrors > Home > ILE Home > Th. List > rexsns | Unicode version |
Description: Restricted existential quantification over a singleton. (Contributed by Mario Carneiro, 23-Apr-2015.) (Revised by NM, 22-Aug-2018.) |
Ref | Expression |
---|---|
rexsns |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | velsn 3467 |
. . . 4
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2 | 1 | anbi1i 447 |
. . 3
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3 | 2 | exbii 1542 |
. 2
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4 | df-rex 2366 |
. 2
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5 | sbc5 2864 |
. 2
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6 | 3, 4, 5 | 3bitr4i 211 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-rex 2366 df-v 2622 df-sbc 2842 df-sn 3456 |
This theorem is referenced by: rexsng 3488 r19.12sn 3512 iunxsngf 3813 finexdc 6672 exfzdc 9705 |
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