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Mirrors > Home > ILE Home > Th. List > Mathboxes > strcollnf | Unicode version |
Description: Version of ax-strcoll 15137 with one disjoint variable condition
removed,
the other disjoint variable condition replaced with a nonfreeness
hypothesis, and without initial universal quantifier. Version of
strcoll2 15138 with the disjoint variable condition on ![]() ![]() ![]()
This proof aims to demonstrate a standard technique, but strcoll2 15138 will
generally suffice: since the theorem asserts the existence of a set
|
Ref | Expression |
---|---|
strcollnf.nf |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
strcollnf |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | strcollnft 15139 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | strcollnf.nf |
. . 3
![]() ![]() ![]() ![]() | |
3 | 2 | ax-gen 1460 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() |
4 | 1, 3 | mpg 1462 |
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 2171 ax-strcoll 15137 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 |
This theorem is referenced by: (None) |
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