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Mirrors > Home > ILE Home > Th. List > uniex | Unicode version |
Description: The Axiom of Union in
class notation. This says that if ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
uniex.1 |
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Ref | Expression |
---|---|
uniex |
![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uniex.1 |
. 2
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2 | unieq 3753 |
. . 3
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3 | 2 | eleq1d 2209 |
. 2
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4 | uniex2 4366 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 4 | issetri 2698 |
. 2
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6 | 1, 3, 5 | vtocl 2743 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-un 4363 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rex 2423 df-v 2691 df-uni 3745 |
This theorem is referenced by: vuniex 4368 uniexg 4369 unex 4370 uniuni 4380 iunpw 4409 fo1st 6063 fo2nd 6064 brtpos2 6156 tfrexlem 6239 ixpsnf1o 6638 xpcomco 6728 xpassen 6732 pnfnre 7831 pnfxr 7842 |
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