Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > vtocldf | Unicode version |
Description: Implicit substitution of a class for a setvar variable. (Contributed by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
vtocld.1 | |
vtocld.2 | |
vtocld.3 | |
vtocldf.4 | |
vtocldf.5 | |
vtocldf.6 |
Ref | Expression |
---|---|
vtocldf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vtocldf.5 | . 2 | |
2 | vtocldf.6 | . 2 | |
3 | vtocldf.4 | . . 3 | |
4 | vtocld.2 | . . . 4 | |
5 | 4 | ex 114 | . . 3 |
6 | 3, 5 | alrimi 1515 | . 2 |
7 | vtocld.3 | . . 3 | |
8 | 3, 7 | alrimi 1515 | . 2 |
9 | vtocld.1 | . 2 | |
10 | vtoclgft 2780 | . 2 | |
11 | 1, 2, 6, 8, 9, 10 | syl221anc 1244 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1346 wceq 1348 wnf 1453 wcel 2141 wnfc 2299 |
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-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 |
This theorem is referenced by: vtocld 2782 peano2 4577 iota2df 5182 |
Copyright terms: Public domain | W3C validator |