![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > 3anbi123i | Unicode version |
Description: Join 3 biconditionals with conjunction. (Contributed by NM, 21-Apr-1994.) |
Ref | Expression |
---|---|
bi3.1 |
![]() ![]() ![]() ![]() ![]() ![]() |
bi3.2 |
![]() ![]() ![]() ![]() ![]() ![]() |
bi3.3 |
![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
3anbi123i |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bi3.1 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() | |
2 | bi3.2 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 1, 2 | anbi12i 453 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | bi3.3 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 3, 4 | anbi12i 453 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | df-3an 947 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | df-3an 947 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | 5, 6, 7 | 3bitr4i 211 |
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 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-3an 947 |
This theorem is referenced by: 3anbi1i 1155 3anbi2i 1156 3anbi3i 1157 syl3anb 1242 ne3anior 2370 isstructim 11816 |
Copyright terms: Public domain | W3C validator |