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Mirrors > Home > NFE Home > Th. List > orbi2i | Unicode version |
Description: Inference adding a left disjunct to both sides of a logical equivalence. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 12-Dec-2012.) |
Ref | Expression |
---|---|
orbi2i.1 |
Ref | Expression |
---|---|
orbi2i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orbi2i.1 | . . . 4 | |
2 | 1 | biimpi 186 | . . 3 |
3 | 2 | orim2i 504 | . 2 |
4 | 1 | biimpri 197 | . . 3 |
5 | 4 | orim2i 504 | . 2 |
6 | 3, 5 | impbii 180 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 176 wo 357 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 177 df-or 359 |
This theorem is referenced by: orbi1i 506 orbi12i 507 orass 510 or4 514 or42 515 orordir 517 dn1 932 3orcomb 944 excxor 1309 cad1 1398 nf4 1868 19.44 1877 exmidne 2522 r19.30 2756 sspsstri 3371 unass 3420 undi 3502 undif3 3515 undif4 3607 ssunpr 3868 sspr 3869 sstp 3870 iinun2 4032 iinuni 4049 axtyplowerprim 4094 pwadjoin 4119 nnsucelrlem2 4425 ltfintrilem1 4465 nnadjoin 4520 dfphi2 4569 phi011lem1 4598 clos1baseima 5883 clos1basesucg 5884 fce 6188 |
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