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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 2218 | . 2 |
5 | 1, 4 | eqeltrrd 2217 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 |
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 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-4 1487 ax-17 1506 ax-ial 1514 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-cleq 2132 df-clel 2135 |
This theorem is referenced by: reg3exmidlemwe 4493 nnaordi 6404 icoshftf1o 9774 lincmb01cmp 9786 fzosubel 9971 cnmpt2res 12466 dvcnp2cntop 12832 |
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