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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 | |
3eltr3d.2 | |
3eltr3d.3 |
Ref | Expression |
---|---|
3eltr3d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3eltr3d.2 | . 2 | |
2 | 3eltr3d.1 | . . 3 | |
3 | 3eltr3d.3 | . . 3 | |
4 | 2, 3 | eleqtrd 2116 | . 2 |
5 | 1, 4 | eqeltrrd 2115 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 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: reg3exmidlemwe 4303 nnaordi 6081 icoshftf1o 8859 lincmb01cmp 8871 fzosubel 9050 |
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