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Mirrors > Home > ILE Home > Th. List > dfss2f | Unicode version |
Description: Equivalence for subclass relation, using bound-variable hypotheses instead of distinct variable conditions. (Contributed by NM, 3-Jul-1994.) (Revised by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
dfss2f.1 |
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dfss2f.2 |
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Ref | Expression |
---|---|
dfss2f |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfss2 3091 |
. 2
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2 | dfss2f.1 |
. . . . 5
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3 | 2 | nfcri 2276 |
. . . 4
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4 | dfss2f.2 |
. . . . 5
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5 | 4 | nfcri 2276 |
. . . 4
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6 | 3, 5 | nfim 1552 |
. . 3
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7 | nfv 1509 |
. . 3
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8 | eleq1 2203 |
. . . 4
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9 | eleq1 2203 |
. . . 4
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10 | 8, 9 | imbi12d 233 |
. . 3
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11 | 6, 7, 10 | cbval 1728 |
. 2
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12 | 1, 11 | bitri 183 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-in 3082 df-ss 3089 |
This theorem is referenced by: dfss3f 3094 ssrd 3107 ssrmof 3165 ss2ab 3170 |
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