![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > eleq12i | Unicode version |
Description: Inference from equality to equivalence of membership. (Contributed by NM, 31-May-1994.) |
Ref | Expression |
---|---|
eleq1i.1 |
![]() ![]() ![]() ![]() |
eleq12i.2 |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
eleq12i |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq12i.2 |
. . 3
![]() ![]() ![]() ![]() | |
2 | 1 | eleq2i 2244 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3 | eleq1i.1 |
. . 3
![]() ![]() ![]() ![]() | |
4 | 3 | eleq1i 2243 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | 2, 4 | bitri 184 |
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-5 1447 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-4 1510 ax-17 1526 ax-ial 1534 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-cleq 2170 df-clel 2173 |
This theorem is referenced by: 3eltr3g 2262 3eltr4g 2263 sbcel12g 3072 ennnfonelem1 12378 |
Copyright terms: Public domain | W3C validator |