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Mirrors > Home > ILE Home > Th. List > ralcom | Unicode version |
Description: Commutation of restricted quantifiers. (Contributed by NM, 13-Oct-1999.) (Revised by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
ralcom |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2331 |
. 2
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2 | nfcv 2331 |
. 2
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3 | 1, 2 | ralcomf 2650 |
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 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2170 |
This theorem depends on definitions: df-bi 117 df-nf 1471 df-sb 1773 df-cleq 2181 df-clel 2184 df-nfc 2320 df-ral 2472 |
This theorem is referenced by: ralrot3 2654 ralcom4 2773 ssint 3874 issod 4333 reusv3 4474 cnvpom 5185 cnvsom 5186 fununi 5298 isocnv2 5828 dfsmo2 6305 ixpiinm 6741 rexfiuz 11015 isnsg2 13107 opprsubrngg 13518 rmodislmodlem 13626 rmodislmod 13627 tgss2 13962 cnmptcom 14181 |
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