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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 2183 |
. 2
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2 | nfsab1 2179 |
. . . 4
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3 | nfsab1 2179 |
. . . 4
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4 | 2, 3 | nfbi 1600 |
. . 3
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5 | nfv 1539 |
. . 3
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6 | df-clab 2176 |
. . . . 5
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7 | sbequ12r 1783 |
. . . . 5
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8 | 6, 7 | bitrid 192 |
. . . 4
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9 | df-clab 2176 |
. . . . 5
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10 | sbequ12r 1783 |
. . . . 5
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11 | 9, 10 | bitrid 192 |
. . . 4
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12 | 8, 11 | bibi12d 235 |
. . 3
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13 | 4, 5, 12 | cbval 1765 |
. 2
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14 | 1, 13 | bitr2i 185 |
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-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 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-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 |
This theorem is referenced by: abbii 2305 abbid 2306 rabbi 2668 sbcbi2 3028 dfiota2 5197 iotabi 5205 uniabio 5206 |
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