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Mirrors > Home > ILE Home > Th. List > clelsb4 | Unicode version |
Description: Substitution applied to an atomic wff (class version of elsb4 2133). (Contributed by Jim Kingdon, 22-Nov-2018.) |
Ref | Expression |
---|---|
clelsb4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1505 |
. . 3
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2 | 1 | sbco2 1942 |
. 2
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3 | nfv 1505 |
. . . 4
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4 | eleq2 2218 |
. . . 4
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5 | 3, 4 | sbie 1768 |
. . 3
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6 | 5 | sbbii 1742 |
. 2
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7 | nfv 1505 |
. . 3
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8 | eleq2 2218 |
. . 3
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9 | 7, 8 | sbie 1768 |
. 2
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10 | 2, 6, 9 | 3bitr3i 209 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1481 ax-10 1482 ax-11 1483 ax-i12 1484 ax-bndl 1486 ax-4 1487 ax-17 1503 ax-i9 1507 ax-ial 1511 ax-i5r 1512 ax-ext 2136 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1740 df-cleq 2147 df-clel 2150 |
This theorem is referenced by: peano1 4547 peano2 4548 |
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