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Mirrors > Home > ILE Home > Th. List > onsucelsucexmidlem1 | Unicode version |
Description: Lemma for onsucelsucexmid 4383. (Contributed by Jim Kingdon, 2-Aug-2019.) |
Ref | Expression |
---|---|
onsucelsucexmidlem1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0ex 3995 |
. . 3
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2 | 1 | prid1 3576 |
. 2
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3 | eqid 2100 |
. . 3
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4 | 3 | orci 691 |
. 2
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5 | eqeq1 2106 |
. . . 4
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6 | 5 | orbi1d 746 |
. . 3
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7 | 6 | elrab 2793 |
. 2
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8 | 2, 4, 7 | mpbir2an 894 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 584 ax-in2 585 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-nul 3994 |
This theorem depends on definitions: df-bi 116 df-tru 1302 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-rab 2384 df-v 2643 df-dif 3023 df-un 3025 df-nul 3311 df-sn 3480 df-pr 3481 |
This theorem is referenced by: onsucelsucexmidlem 4382 onsucelsucexmid 4383 acexmidlem2 5703 |
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