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Mirrors > Home > ILE Home > Th. List > raleq | Unicode version |
Description: Equality theorem for restricted universal quantifier. (Contributed by NM, 16-Nov-1995.) |
Ref | Expression |
---|---|
raleq |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2336 |
. 2
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2 | nfcv 2336 |
. 2
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3 | 1, 2 | raleqf 2686 |
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-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2175 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-cleq 2186 df-clel 2189 df-nfc 2325 df-ral 2477 |
This theorem is referenced by: raleqi 2694 raleqdv 2696 raleqbi1dv 2702 sbralie 2744 inteq 3874 iineq1 3927 bnd2 4203 frforeq2 4377 weeq2 4389 ordeq 4404 reg2exmid 4569 reg3exmid 4613 omsinds 4655 fncnv 5321 funimaexglem 5338 isoeq4 5848 acexmidlemv 5917 tfrlem1 6363 tfr0dm 6377 tfrlemisucaccv 6380 tfrlemi1 6387 tfrlemi14d 6388 tfrexlem 6389 tfr1onlemsucaccv 6396 tfr1onlemaccex 6403 tfr1onlemres 6404 tfrcllemsucaccv 6409 tfrcllembxssdm 6411 tfrcllemaccex 6416 tfrcllemres 6417 tfrcldm 6418 ixpeq1 6765 ac6sfi 6956 fimax2gtri 6959 dcfi 7042 supeq1 7047 supeq2 7050 nnnninfeq2 7190 isomni 7197 ismkv 7214 iswomni 7226 tapeq2 7315 sup3exmid 8978 rexanuz 11135 rexfiuz 11136 fimaxre2 11373 modfsummod 11604 mhmpropd 13041 isghm 13316 iscmn 13366 srgideu 13471 dfrhm2 13653 cnprcl2k 14385 ispsmet 14502 ismet 14523 isxmet 14524 cncfval 14751 dvcn 14879 setindis 15529 bdsetindis 15531 strcoll2 15545 strcollnfALT 15548 |
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