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Mirrors > Home > ILE Home > Th. List > iuneq12d | Unicode version |
Description: Equality deduction for indexed union, deduction version. (Contributed by Drahflow, 22-Oct-2015.) |
Ref | Expression |
---|---|
iuneq1d.1 |
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iuneq12d.2 |
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Ref | Expression |
---|---|
iuneq12d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iuneq1d.1 |
. . 3
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2 | 1 | iuneq1d 3909 |
. 2
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3 | iuneq12d.2 |
. . . 4
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4 | 3 | adantr 276 |
. . 3
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5 | 4 | iuneq2dv 3907 |
. 2
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6 | 2, 5 | eqtrd 2210 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-in 3135 df-ss 3142 df-iun 3888 |
This theorem is referenced by: rdgivallem 6381 rdgon 6386 rdg0 6387 imasival 12709 reldvg 14041 dvfvalap 14043 |
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