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Mirrors > Home > ILE Home > Th. List > clelsb2 | Unicode version |
Description: Substitution for the second argument of the membership predicate in an atomic formula (class version of elsb2 2168). (Contributed by Jim Kingdon, 22-Nov-2018.) |
Ref | Expression |
---|---|
clelsb2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1539 |
. . 3
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2 | 1 | sbco2 1977 |
. 2
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3 | nfv 1539 |
. . . 4
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4 | eleq2 2253 |
. . . 4
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5 | 3, 4 | sbie 1802 |
. . 3
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6 | 5 | sbbii 1776 |
. 2
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7 | nfv 1539 |
. . 3
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8 | eleq2 2253 |
. . 3
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9 | 7, 8 | sbie 1802 |
. 2
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10 | 2, 6, 9 | 3bitr3i 210 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-cleq 2182 df-clel 2185 |
This theorem is referenced by: peano1 4608 peano2 4609 |
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