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Mirrors > Home > ILE Home > Th. List > clelsb1f | Unicode version |
Description: Substitution for the first argument of the membership predicate in an atomic formula (class version of elsb1 2165). (Contributed by Rodolfo Medina, 28-Apr-2010.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) (Revised by Thierry Arnoux, 13-Mar-2017.) |
Ref | Expression |
---|---|
clelsb1f.1 |
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Ref | Expression |
---|---|
clelsb1f |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clelsb1f.1 |
. . . 4
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2 | 1 | nfcri 2323 |
. . 3
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3 | 2 | sbco2 1975 |
. 2
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4 | nfv 1538 |
. . . 4
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5 | eleq1w 2248 |
. . . 4
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6 | 4, 5 | sbie 1801 |
. . 3
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7 | 6 | sbbii 1775 |
. 2
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8 | nfv 1538 |
. . 3
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9 | eleq1w 2248 |
. . 3
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10 | 8, 9 | sbie 1801 |
. 2
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11 | 3, 7, 10 | 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 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-nf 1471 df-sb 1773 df-cleq 2180 df-clel 2183 df-nfc 2318 |
This theorem is referenced by: rmo3f 2946 |
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