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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 2184 | . 2 |
4 | 1, 3 | mpbi 144 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1316 wcel 1465 |
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 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-4 1472 ax-17 1491 ax-ial 1499 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-cleq 2110 df-clel 2113 |
This theorem is referenced by: eleqtrri 2193 3eltr3i 2198 prid2 3600 2eluzge0 9338 fz01or 9859 ef0lem 11293 ege2le3 11304 efgt1p2 11328 efgt1p 11329 phi1 11822 cnrehmeocntop 12689 dvcjbr 12768 |
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