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Mirrors > Home > ILE Home > Th. List > bibi2i | Unicode version |
Description: Inference adding a biconditional to the left in an equivalence. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 7-May-2011.) (Proof shortened by Wolf Lammen, 16-May-2013.) |
Ref | Expression |
---|---|
bibi.a |
Ref | Expression |
---|---|
bibi2i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . . 3 | |
2 | bibi.a | . . 3 | |
3 | 1, 2 | bitrdi 195 | . 2 |
4 | id 19 | . . 3 | |
5 | 4, 2 | bitr4di 197 | . 2 |
6 | 3, 5 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: bibi1i 227 bibi12i 228 bibi2d 231 pm4.71r 388 sblbis 1953 sbrbif 1955 abeq2 2279 abid2f 2338 necon4biddc 2415 pm13.183 2868 disj3 3466 euabsn2 3650 a9evsep 4109 inex1 4121 zfpair2 4193 sucel 4393 bdinex1 13894 bj-zfpair2 13905 bj-d0clsepcl 13920 |
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