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Mirrors > Home > ILE Home > Th. List > 3eltr3g | Unicode version |
Description: Substitution of equal classes into membership relation. (Contributed by Mario Carneiro, 6-Jan-2017.) |
Ref | Expression |
---|---|
3eltr3g.1 |
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3eltr3g.2 |
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3eltr3g.3 |
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Ref | Expression |
---|---|
3eltr3g |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3eltr3g.1 |
. 2
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2 | 3eltr3g.2 |
. . 3
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3 | 3eltr3g.3 |
. . 3
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4 | 2, 3 | eleq12i 2255 |
. 2
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5 | 1, 4 | sylib 122 |
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-5 1457 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-4 1520 ax-17 1536 ax-ial 1544 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-cleq 2180 df-clel 2183 |
This theorem is referenced by: (None) |
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