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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfcleq 2171 |
. . . . . 6
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2 | 1 | biimpi 120 |
. . . . 5
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3 | 2 | 19.21bi 1558 |
. . . 4
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4 | 3 | anbi2d 464 |
. . 3
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5 | 4 | exbidv 1825 |
. 2
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6 | df-clel 2173 |
. 2
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7 | df-clel 2173 |
. 2
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8 | 5, 6, 7 | 3bitr4g 223 |
1
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