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Mirrors > Home > ILE Home > Th. List > inv1 | Unicode version |
Description: The intersection of a class with the universal class is itself. Exercise 4.10(k) of [Mendelson] p. 231. (Contributed by NM, 17-May-1998.) |
Ref | Expression |
---|---|
inv1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inss1 3262 |
. 2
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2 | ssid 3083 |
. . 3
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3 | ssv 3085 |
. . 3
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4 | 2, 3 | ssini 3265 |
. 2
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5 | 1, 4 | eqssi 3079 |
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-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-v 2659 df-in 3043 df-ss 3050 |
This theorem is referenced by: rint0 3776 riin0 3850 xpssres 4812 resdmdfsn 4820 imainrect 4942 xpima2m 4944 dmresv 4955 |
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