![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > syl5eleq | Unicode version |
Description: B membership and equality inference. (Contributed by NM, 4-Jan-2006.) |
Ref | Expression |
---|---|
syl5eleq.1 |
![]() ![]() ![]() ![]() |
syl5eleq.2 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
syl5eleq |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl5eleq.1 |
. . 3
![]() ![]() ![]() ![]() | |
2 | 1 | a1i 9 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3 | syl5eleq.2 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 2, 3 | eleqtrd 2113 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-4 1397 ax-17 1416 ax-ial 1424 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-cleq 2030 df-clel 2033 |
This theorem is referenced by: syl5eleqr 2124 opth1 3964 opth 3965 eqelsuc 4122 bj-nnelirr 9413 |
Copyright terms: Public domain | W3C validator |