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Mirrors > Home > MPE Home > Th. List > elrabi | Structured version Visualization version Unicode version |
Description: Implication for the membership in a restricted class abstraction. (Contributed by Alexander van der Vekens, 31-Dec-2017.) |
Ref | Expression |
---|---|
elrabi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clelab 2748 | . . 3 | |
2 | eleq1 2689 | . . . . . 6 | |
3 | 2 | anbi1d 741 | . . . . 5 |
4 | 3 | simprbda 653 | . . . 4 |
5 | 4 | exlimiv 1858 | . . 3 |
6 | 1, 5 | sylbi 207 | . 2 |
7 | df-rab 2921 | . 2 | |
8 | 6, 7 | eleq2s 2719 | 1 |
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