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Mirrors > Home > ILE Home > Th. List > ralsnsg | Unicode version |
Description: Substitution expressed in terms of quantification over a singleton. (Contributed by NM, 14-Dec-2005.) (Revised by Mario Carneiro, 23-Apr-2015.) |
Ref | Expression |
---|---|
ralsnsg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbc6g 2933 | . 2 | |
2 | df-ral 2421 | . . 3 | |
3 | velsn 3544 | . . . . 5 | |
4 | 3 | imbi1i 237 | . . . 4 |
5 | 4 | albii 1446 | . . 3 |
6 | 2, 5 | bitri 183 | . 2 |
7 | 1, 6 | syl6rbbr 198 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1329 wceq 1331 wcel 1480 wral 2416 wsbc 2909 csn 3527 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-v 2688 df-sbc 2910 df-sn 3533 |
This theorem is referenced by: ixpsnval 6595 ac6sfi 6792 rexfiuz 10761 prmind2 11801 |
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