Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > sbal1 | Unicode version |
Description: A theorem used in elimination of disjoint variable conditions on by replacing it with a distinctor . (Contributed by NM, 5-Aug-1993.) (Proof rewitten by Jim Kingdon, 24-Feb-2018.) |
Ref | Expression |
---|---|
sbal1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbal 1953 | . . . 4 | |
2 | 1 | sbbii 1723 | . . 3 |
3 | sbal1yz 1954 | . . 3 | |
4 | 2, 3 | syl5bb 191 | . 2 |
5 | ax-17 1491 | . . 3 | |
6 | 5 | sbco2v 1898 | . 2 |
7 | ax-17 1491 | . . . 4 | |
8 | 7 | sbco2v 1898 | . . 3 |
9 | 8 | albii 1431 | . 2 |
10 | 4, 6, 9 | 3bitr3g 221 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wal 1314 wsb 1720 |
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-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |