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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 | syl6bb 195 | . 2 |
4 | id 19 | . . 3 | |
5 | 4, 2 | syl6bbr 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 387 sblbis 1933 sbrbif 1935 abeq2 2248 abid2f 2306 necon4biddc 2383 pm13.183 2822 disj3 3415 euabsn2 3592 a9evsep 4050 inex1 4062 zfpair2 4132 sucel 4332 bdinex1 13097 bj-zfpair2 13108 bj-d0clsepcl 13123 |
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