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Mirrors > Home > ILE Home > Th. List > clelsb3 | Unicode version |
Description: Substitution applied to an atomic wff (class version of elsb3 1929). (Contributed by Rodolfo Medina, 28-Apr-2010.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) |
Ref | Expression |
---|---|
clelsb3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1493 | . . 3 | |
2 | 1 | sbco2 1916 | . 2 |
3 | nfv 1493 | . . . 4 | |
4 | eleq1 2180 | . . . 4 | |
5 | 3, 4 | sbie 1749 | . . 3 |
6 | 5 | sbbii 1723 | . 2 |
7 | nfv 1493 | . . 3 | |
8 | eleq1 2180 | . . 3 | |
9 | 7, 8 | sbie 1749 | . 2 |
10 | 2, 6, 9 | 3bitr3i 209 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wcel 1465 wsb 1720 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-cleq 2110 df-clel 2113 |
This theorem is referenced by: hblem 2225 nfraldya 2446 nfrexdya 2447 cbvreu 2629 sbcel1v 2943 rmo3 2972 setindel 4423 elirr 4426 en2lp 4439 zfregfr 4458 tfi 4466 bdcriota 13008 |
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