Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > equsal | Unicode version |
Description: A useful equivalence related to substitution. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 12-Aug-2011.) (Revised by Mario Carneiro, 3-Oct-2016.) (Proof shortened by Wolf Lammen, 5-Feb-2018.) |
Ref | Expression |
---|---|
equsal.1 | |
equsal.2 |
Ref | Expression |
---|---|
equsal |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equsal.1 | . . 3 | |
2 | 1 | 19.23 1608 | . 2 |
3 | equsal.2 | . . . 4 | |
4 | 3 | pm5.74i 178 | . . 3 |
5 | 4 | albii 1399 | . 2 |
6 | a9e 1626 | . . 3 | |
7 | 6 | a1bi 241 | . 2 |
8 | 2, 5, 7 | 3bitr4i 210 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 wal 1282 wnf 1389 wex 1421 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-i9 1463 ax-ial 1467 ax-i5r 1468 |
This theorem depends on definitions: df-bi 115 df-nf 1390 |
This theorem is referenced by: intirr 4731 fun11 4986 |
Copyright terms: Public domain | W3C validator |