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Mirrors > Home > ILE Home > Th. List > ralcom4 | Unicode version |
Description: Commutation of restricted and unrestricted universal quantifiers. (Contributed by NM, 26-Mar-2004.) (Proof shortened by Andrew Salmon, 8-Jun-2011.) |
Ref | Expression |
---|---|
ralcom4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralcom 2530 |
. 2
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2 | ralv 2636 |
. . 3
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3 | 2 | ralbii 2384 |
. 2
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4 | ralv 2636 |
. 2
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5 | 1, 3, 4 | 3bitr3i 208 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ral 2364 df-v 2621 |
This theorem is referenced by: uniiunlem 3109 uni0b 3678 iunss 3771 disjnim 3836 trint 3951 reliun 4558 funimass4 5355 ralrnmpt2 5759 |
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