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Mirrors > Home > NFE Home > Th. List > eqeltrrd | Unicode version |
Description: Deduction that substitutes equal classes into membership. (Contributed by NM, 14-Dec-2004.) |
Ref | Expression |
---|---|
eqeltrrd.1 | |
eqeltrrd.2 |
Ref | Expression |
---|---|
eqeltrrd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeltrrd.1 | . . 3 | |
2 | 1 | eqcomd 2358 | . 2 |
3 | eqeltrrd.2 | . 2 | |
4 | 2, 3 | eqeltrd 2427 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1642 wcel 1710 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-11 1746 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 df-cleq 2346 df-clel 2349 |
This theorem is referenced by: 3eltr3d 2433 nnsucelr 4428 sfinltfin 4535 vfin1cltv 4547 vfinspsslem1 4550 phi11lem1 4595 xpexr2 5110 ffvresb 5431 ncdisjun 6136 eqtc 6161 |
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