![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > 3bitr2rd | Unicode version |
Description: Deduction from transitivity of biconditional. (Contributed by NM, 4-Aug-2006.) |
Ref | Expression |
---|---|
3bitr2d.1 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3bitr2d.2 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3bitr2d.3 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
3bitr2rd |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3bitr2d.1 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | 3bitr2d.2 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 1, 2 | bitr4d 191 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | 3bitr2d.3 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 3, 4 | bitr2d 189 |
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: fndmdif 5616 addsubeq4 8149 muleqadd 8601 nn0lt10b 9309 adddivflid 10265 frec2uzltd 10376 mul0inf 11220 summodnegmod 11800 lgsdilem 14061 lgsne0 14072 iooref1o 14405 |
Copyright terms: Public domain | W3C validator |