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Mirrors > Home > MPE Home > Th. List > abbi | Structured version Visualization version Unicode version |
Description: Equivalent wff's correspond to equal class abstractions. (Contributed by NM, 25-Nov-2013.) (Revised by Mario Carneiro, 11-Aug-2016.) (Proof shortened by Wolf Lammen, 16-Nov-2019.) |
Ref | Expression |
---|---|
abbi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbab1 2451 |
. . 3
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2 | hbab1 2451 |
. . 3
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3 | 1, 2 | cleqh 2563 |
. 2
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4 | abid 2450 |
. . . 4
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5 | abid 2450 |
. . . 4
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6 | 4, 5 | bibi12i 321 |
. . 3
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7 | 6 | albii 1702 |
. 2
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8 | 3, 7 | bitr2i 258 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 |
This theorem depends on definitions: df-bi 190 df-an 377 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-clab 2449 df-cleq 2455 df-clel 2458 |
This theorem is referenced by: abbii 2578 abbid 2579 nabbi 2737 rabbi 2981 sbcbi2 3328 rabeqsn 4013 iuneq12df 4316 dfiota2 5570 iotabi 5578 uniabio 5579 iotanul 5584 karden 8397 iuneq12daf 28225 bj-cleq 31601 abeq12 32445 elnev 36834 csbingVD 37322 csbsngVD 37331 csbxpgVD 37332 csbrngVD 37334 csbunigVD 37336 csbfv12gALTVD 37337 |
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