![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > vtoclgf | Unicode version |
Description: Implicit substitution of a class for a setvar variable, with bound-variable hypotheses in place of distinct variable restrictions. (Contributed by NM, 21-Sep-2003.) (Proof shortened by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
vtoclgf.1 |
![]() ![]() ![]() ![]() |
vtoclgf.2 |
![]() ![]() ![]() ![]() |
vtoclgf.3 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
vtoclgf.4 |
![]() ![]() |
Ref | Expression |
---|---|
vtoclgf |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2763 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | vtoclgf.1 |
. . . 4
![]() ![]() ![]() ![]() | |
3 | 2 | issetf 2759 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | vtoclgf.2 |
. . . 4
![]() ![]() ![]() ![]() | |
5 | vtoclgf.4 |
. . . . 5
![]() ![]() | |
6 | vtoclgf.3 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 5, 6 | mpbii 148 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | 4, 7 | exlimi 1605 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | 3, 8 | sylbi 121 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
10 | 1, 9 | syl 14 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 |
This theorem is referenced by: vtoclg 2812 vtocl2gf 2814 vtocl3gf 2815 vtoclgaf 2817 ceqsexg 2880 elabgf 2894 mob 2934 opeliunxp2 4785 fvmptss2 5612 |
Copyright terms: Public domain | W3C validator |