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Mirrors > Home > ILE Home > Th. List > Mathboxes > strcollnfALT | Unicode version |
Description: Alternate proof of strcollnf 15190, not using strcollnft 15189. (Contributed by BJ, 5-Oct-2019.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
strcollnf.nf |
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Ref | Expression |
---|---|
strcollnfALT |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | strcoll2 15188 |
. 2
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2 | nfcv 2332 |
. . . . 5
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3 | nfcv 2332 |
. . . . . 6
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4 | strcollnf.nf |
. . . . . 6
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5 | 3, 4 | nfrexxy 2529 |
. . . . 5
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6 | 2, 5 | nfralxy 2528 |
. . . 4
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7 | 2, 4 | nfrexxy 2529 |
. . . . 5
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8 | 3, 7 | nfralxy 2528 |
. . . 4
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9 | 6, 8 | nfan 1576 |
. . 3
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10 | nfv 1539 |
. . . 4
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11 | nfv 1539 |
. . . 4
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12 | 10, 11 | nfan 1576 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
13 | rexeq 2687 |
. . . . 5
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14 | 13 | ralbidv 2490 |
. . . 4
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15 | raleq 2686 |
. . . 4
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16 | 14, 15 | anbi12d 473 |
. . 3
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17 | 9, 12, 16 | cbvex 1767 |
. 2
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18 | 1, 17 | sylib 122 |
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 15187 |
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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