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Mirrors > Home > ILE Home > Th. List > abbi | Unicode version |
Description: Equivalent wff's correspond to equal class abstractions. (Contributed by NM, 25-Nov-2013.) (Revised by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
abbi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfcleq 2082 |
. 2
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2 | nfsab1 2078 |
. . . 4
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3 | nfsab1 2078 |
. . . 4
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4 | 2, 3 | nfbi 1526 |
. . 3
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5 | nfv 1466 |
. . 3
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6 | df-clab 2075 |
. . . . 5
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7 | sbequ12r 1702 |
. . . . 5
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8 | 6, 7 | syl5bb 190 |
. . . 4
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9 | df-clab 2075 |
. . . . 5
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10 | sbequ12r 1702 |
. . . . 5
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11 | 9, 10 | syl5bb 190 |
. . . 4
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12 | 8, 11 | bibi12d 233 |
. . 3
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13 | 4, 5, 12 | cbval 1684 |
. 2
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14 | 1, 13 | bitr2i 183 |
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 104 ax-ia2 105 ax-ia3 106 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-11 1442 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 |
This theorem is referenced by: abbii 2203 abbid 2204 rabbi 2544 sbcbi2 2889 dfiota2 4981 iotabi 4989 uniabio 4990 |
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