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Mirrors > Home > MPE Home > Th. List > sbcel1g | Structured version Visualization version Unicode version |
Description: Move proper substitution
in and out of a membership relation. Note that
the scope of ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
sbcel1g |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcel12 3783 |
. 2
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2 | csbconstg 3387 |
. . 3
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3 | 2 | eleq2d 2524 |
. 2
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4 | 1, 3 | syl5bb 265 |
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-11 1930 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-fal 1460 df-ex 1674 df-nf 1678 df-sb 1808 df-clab 2448 df-cleq 2454 df-clel 2457 df-nfc 2591 df-v 3058 df-sbc 3279 df-csb 3375 df-dif 3418 df-in 3422 df-ss 3429 df-nul 3743 |
This theorem is referenced by: rspcsbela 3806 fprodcllemf 14060 wunnat 15909 catcfuccl 16052 nbgraopALT 25200 rusgrasn 25721 esumpfinvalf 28945 esum2dlem 28961 measiuns 29087 bj-sbel1 31551 csbopg2 31769 csbfinxpg 31824 finixpnum 31974 renegclALT 32579 cdlemk35s 34548 ellimcabssub0 37734 |
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