Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > eqvincg | Unicode version |
Description: A variable introduction law for class equality, deduction version. (Contributed by Thierry Arnoux, 2-Mar-2017.) |
Ref | Expression |
---|---|
eqvincg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2744 | . . . 4 | |
2 | ax-1 6 | . . . . . 6 | |
3 | eqtr 2188 | . . . . . . 7 | |
4 | 3 | ex 114 | . . . . . 6 |
5 | 2, 4 | jca 304 | . . . . 5 |
6 | 5 | eximi 1593 | . . . 4 |
7 | pm3.43 597 | . . . . 5 | |
8 | 7 | eximi 1593 | . . . 4 |
9 | 1, 6, 8 | 3syl 17 | . . 3 |
10 | nfv 1521 | . . . 4 | |
11 | 10 | 19.37-1 1667 | . . 3 |
12 | 9, 11 | syl 14 | . 2 |
13 | eqtr2 2189 | . . 3 | |
14 | 13 | exlimiv 1591 | . 2 |
15 | 12, 14 | impbid1 141 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 wex 1485 wcel 2141 |
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-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-v 2732 |
This theorem is referenced by: dff13 5744 f1eqcocnv 5767 |
Copyright terms: Public domain | W3C validator |