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Mirrors > Home > MPE Home > Th. List > sbcan | Structured version Visualization version Unicode version |
Description: Distribution of class substitution over conjunction. (Contributed by NM, 31-Dec-2016.) (Revised by NM, 17-Aug-2018.) |
Ref | Expression |
---|---|
sbcan |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcex 3288 |
. 2
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2 | sbcex 3288 |
. . 3
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3 | 2 | adantl 472 |
. 2
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4 | dfsbcq2 3281 |
. . 3
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5 | dfsbcq2 3281 |
. . . 4
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6 | dfsbcq2 3281 |
. . . 4
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7 | 5, 6 | anbi12d 722 |
. . 3
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8 | sban 2238 |
. . 3
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9 | 4, 7, 8 | vtoclbg 3119 |
. 2
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10 | 1, 3, 9 | pm5.21nii 359 |
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 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-10 1925 ax-12 1943 ax-13 2101 ax-ext 2441 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1457 df-ex 1674 df-nf 1678 df-sb 1808 df-clab 2448 df-cleq 2454 df-clel 2457 df-v 3058 df-sbc 3279 |
This theorem is referenced by: sbc3an 3336 sbcabel 3356 csbuni 4239 csbmpt12 4748 csbxp 4934 difopab 4984 sbcfung 5623 sbcfng 5747 sbcfg 5748 fmptsnd 6109 f1od2 28357 esum2dlem 28961 bnj976 29637 bnj110 29717 bnj1040 29829 csbopg2 31769 csbwrecsg 31772 csboprabg 31775 csbmpt22g 31776 f1omptsnlem 31782 mptsnunlem 31784 relowlpssretop 31811 csbfinxpg 31824 sbcani 32389 sbccom2lem 32408 brtrclfv2 36363 cotrclrcl 36378 frege124d 36397 sbiota1 36828 onfrALTlem5 36951 onfrALTlem4 36952 |
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