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Mirrors > Home > ILE Home > Th. List > elex22 | Unicode version |
Description: If two classes each contain another class, then both contain some set. (Contributed by Alan Sare, 24-Oct-2011.) |
Ref | Expression |
---|---|
elex22 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1a 2106 |
. . . 4
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2 | eleq1a 2106 |
. . . 4
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3 | 1, 2 | anim12ii 325 |
. . 3
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4 | 3 | alrimiv 1751 |
. 2
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5 | elisset 2562 |
. . 3
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6 | 5 | adantr 261 |
. 2
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7 | exim 1487 |
. 2
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8 | 4, 6, 7 | sylc 56 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-v 2553 |
This theorem is referenced by: (None) |
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