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Mirrors > Home > ILE Home > Th. List > 3eltr3d | Unicode version |
Description: Substitution of equal classes into membership relation. (Contributed by Mario Carneiro, 6-Jan-2017.) |
Ref | Expression |
---|---|
3eltr3d.1 |
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3eltr3d.2 |
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3eltr3d.3 |
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Ref | Expression |
---|---|
3eltr3d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3eltr3d.2 |
. 2
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2 | 3eltr3d.1 |
. . 3
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3 | 3eltr3d.3 |
. . 3
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4 | 2, 3 | eleqtrd 2219 |
. 2
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5 | 1, 4 | eqeltrrd 2218 |
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-5 1424 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-4 1488 ax-17 1507 ax-ial 1515 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-cleq 2133 df-clel 2136 |
This theorem is referenced by: reg3exmidlemwe 4501 nnaordi 6412 icoshftf1o 9804 lincmb01cmp 9816 fzosubel 10002 cnmpt2res 12505 dvcnp2cntop 12871 |
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