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Mirrors > Home > ILE Home > Th. List > eleqtri | Unicode version |
Description: Substitution of equal classes into membership relation. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
eleqtr.1 | |
eleqtr.2 |
Ref | Expression |
---|---|
eleqtri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleqtr.1 | . 2 | |
2 | eleqtr.2 | . . 3 | |
3 | 2 | eleq2i 2104 | . 2 |
4 | 1, 3 | mpbi 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1243 wcel 1393 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-17 1419 ax-ial 1427 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-cleq 2033 df-clel 2036 |
This theorem is referenced by: eleqtrri 2113 3eltr3i 2118 prid2 3477 2eluzge0 8517 |
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