![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > 3bitr3rd | Unicode version |
Description: Deduction from transitivity of biconditional. (Contributed by NM, 4-Aug-2006.) |
Ref | Expression |
---|---|
3bitr3d.1 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3bitr3d.2 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3bitr3d.3 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
3bitr3rd |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3bitr3d.3 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | 3bitr3d.1 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 3bitr3d.2 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 2, 3 | bitr3d 190 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | 1, 4 | bitr3d 190 |
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 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: funconstss 5634 eqneg 8688 minclpr 11244 evenennn 12393 nmzsubg 13068 rpcxple2 14274 rpcxplt2 14275 lgslem1 14337 |
Copyright terms: Public domain | W3C validator |