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Mirrors > Home > NFE 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 2347 |
. 2
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2 | nfsab1 2343 |
. . . 4
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3 | nfsab1 2343 |
. . . 4
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4 | 2, 3 | nfbi 1834 |
. . 3
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5 | nfv 1619 |
. . 3
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6 | df-clab 2340 |
. . . . 5
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7 | sbequ12r 1920 |
. . . . 5
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8 | 6, 7 | syl5bb 248 |
. . . 4
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9 | df-clab 2340 |
. . . . 5
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10 | sbequ12r 1920 |
. . . . 5
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11 | 9, 10 | syl5bb 248 |
. . . 4
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12 | 8, 11 | bibi12d 312 |
. . 3
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13 | 4, 5, 12 | cbval 1984 |
. 2
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14 | 1, 13 | bitr2i 241 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 |
This theorem is referenced by: abbii 2466 abbid 2467 rabbi 2790 dfeu2 4334 dfiota2 4341 iotabi 4349 uniabio 4350 iotanul 4355 |
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