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Mirrors > Home > ILE Home > Th. List > eleq2 | Unicode version |
Description: Equality implies equivalence of membership. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
eleq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfcleq 2164 | . . . . . 6 | |
2 | 1 | biimpi 119 | . . . . 5 |
3 | 2 | 19.21bi 1551 | . . . 4 |
4 | 3 | anbi2d 461 | . . 3 |
5 | 4 | exbidv 1818 | . 2 |
6 | df-clel 2166 | . 2 | |
7 | df-clel 2166 | . 2 | |
8 | 5, 6, 7 | 3bitr4g 222 | 1 |
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