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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 447 | . . 3 |
4 | bi3.3 | . . 3 | |
5 | 3, 4 | anbi12i 447 | . 2 |
6 | df-3an 921 | . 2 | |
7 | df-3an 921 | . 2 | |
8 | 5, 6, 7 | 3bitr4i 210 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 102 wb 103 w3a 919 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 df-3an 921 |
This theorem is referenced by: 3anbi1i 1129 3anbi2i 1130 3anbi3i 1131 syl3anb 1212 ne3anior 2333 |
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