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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 1947 sbrbif 1949 abeq2 2273 abid2f 2332 necon4biddc 2409 pm13.183 2859 disj3 3456 euabsn2 3639 a9evsep 4098 inex1 4110 zfpair2 4182 sucel 4382 bdinex1 13622 bj-zfpair2 13633 bj-d0clsepcl 13648 |
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