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Mirrors > Home > MPE Home > Th. List > elint | Structured version Unicode version |
Description: Membership in class intersection. (Contributed by NM, 21-May-1994.) |
Ref | Expression |
---|---|
elint.1 |
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Ref | Expression |
---|---|
elint |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elint.1 |
. 2
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2 | eleq1 2526 |
. . . 4
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3 | 2 | imbi2d 316 |
. . 3
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4 | 3 | albidv 1680 |
. 2
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5 | df-int 4240 |
. 2
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6 | 1, 4, 5 | elab2 3216 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 |
This theorem depends on definitions: df-bi 185 df-an 371 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-v 3080 df-int 4240 |
This theorem is referenced by: elint2 4246 elintab 4250 intss1 4254 intss 4260 intun 4271 intpr 4272 cssmre 18246 dfom5b 28107 |
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