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Mirrors > Home > ILE Home > Th. List > clelsb1 | Unicode version |
Description: Substitution for the first argument of the membership predicate in an atomic formula (class version of elsb1 2148). (Contributed by Rodolfo Medina, 28-Apr-2010.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) |
Ref | Expression |
---|---|
clelsb1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1521 | . . 3 | |
2 | 1 | sbco2 1958 | . 2 |
3 | nfv 1521 | . . . 4 | |
4 | eleq1 2233 | . . . 4 | |
5 | 3, 4 | sbie 1784 | . . 3 |
6 | 5 | sbbii 1758 | . 2 |
7 | nfv 1521 | . . 3 | |
8 | eleq1 2233 | . . 3 | |
9 | 7, 8 | sbie 1784 | . 2 |
10 | 2, 6, 9 | 3bitr3i 209 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wsb 1755 wcel 2141 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-cleq 2163 df-clel 2166 |
This theorem is referenced by: hblem 2278 nfraldya 2505 nfrexdya 2506 cbvreu 2694 sbcel1v 3017 rmo3 3046 setindel 4520 elirr 4523 en2lp 4536 zfregfr 4556 tfi 4564 bdcriota 13840 |
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