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Mirrors > Home > ILE Home > Th. List > prssd | Unicode version |
Description: Deduction version of prssi 3776: A pair of elements of a class is a subset of the class. (Contributed by Glauco Siliprandi, 17-Aug-2020.) |
Ref | Expression |
---|---|
prssd.1 |
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prssd.2 |
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Ref | Expression |
---|---|
prssd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prssd.1 |
. 2
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2 | prssd.2 |
. 2
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3 | prssi 3776 |
. 2
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4 | 1, 2, 3 | syl2anc 411 |
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 2175 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-v 2762 df-un 3157 df-in 3159 df-ss 3166 df-sn 3624 df-pr 3625 |
This theorem is referenced by: 0idnsgd 13275 isnzr2 13664 lspprcl 13873 lsptpcl 13874 lspprss 13886 lspprid1 13891 |
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