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Mirrors > Home > MPE Home > Th. List > elin | Structured version Visualization version Unicode version |
Description: Expansion of membership in an intersection of two classes. Theorem 12 of [Suppes] p. 25. (Contributed by NM, 29-Apr-1994.) |
Ref | Expression |
---|---|
elin |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 3054 |
. 2
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2 | elex 3054 |
. . 3
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3 | 2 | adantl 468 |
. 2
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4 | eleq1 2517 |
. . . 4
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5 | eleq1 2517 |
. . . 4
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6 | 4, 5 | anbi12d 717 |
. . 3
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7 | df-in 3411 |
. . 3
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8 | 6, 7 | elab2g 3187 |
. 2
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9 | 1, 3, 8 | pm5.21nii 355 |
1
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