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Mirrors > Home > ILE Home > Th. List > ssequn1 | Unicode version |
Description: A relationship between subclass and union. Theorem 26 of [Suppes] p. 27. (Contributed by NM, 30-Aug-1993.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
ssequn1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bicom 140 |
. . . 4
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2 | pm4.72 828 |
. . . 4
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3 | elun 3291 |
. . . . 5
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4 | 3 | bibi1i 228 |
. . . 4
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5 | 1, 2, 4 | 3bitr4i 212 |
. . 3
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6 | 5 | albii 1481 |
. 2
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7 | dfss2 3159 |
. 2
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8 | dfcleq 2183 |
. 2
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9 | 6, 7, 8 | 3bitr4i 212 |
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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 |
This theorem is referenced by: ssequn2 3323 uniop 4273 pwssunim 4302 unisuc 4431 unisucg 4432 rdgisucinc 6411 oasuc 6490 omsuc 6498 undifdc 6953 |
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