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Mirrors > Home > ILE Home > Th. List > opabss | Unicode version |
Description: The collection of ordered pairs in a class is a subclass of it. (Contributed by NM, 27-Dec-1996.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
---|---|
opabss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-opab 4080 |
. 2
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2 | df-br 4019 |
. . . . 5
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3 | eleq1 2252 |
. . . . . 6
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4 | 3 | biimpar 297 |
. . . . 5
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5 | 2, 4 | sylan2b 287 |
. . . 4
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6 | 5 | exlimivv 1908 |
. . 3
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7 | 6 | abssi 3245 |
. 2
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8 | 1, 7 | eqsstri 3202 |
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-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-in 3150 df-ss 3157 df-br 4019 df-opab 4080 |
This theorem is referenced by: (None) |
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