Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > ifbid | Unicode version |
Description: Equivalence deduction for conditional operators. (Contributed by NM, 18-Apr-2005.) |
Ref | Expression |
---|---|
ifbid.1 |
Ref | Expression |
---|---|
ifbid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ifbid.1 | . 2 | |
2 | ifbi 3462 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1316 cif 3444 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-if 3445 |
This theorem is referenced by: ifbieq1d 3464 ifbieq2d 3466 ifbieq12d 3468 ifandc 3478 fodjum 6986 fodju0 6987 fodjuomni 6989 nnnninf 6991 fodjumkv 7002 xaddval 9583 0tonninf 10167 1tonninf 10168 sumeq1 11079 summodc 11107 zsumdc 11108 fsum3 11111 isumss 11115 sumsplitdc 11156 subctctexmid 13092 nninfalllemn 13098 nninfalllem1 13099 nninfsellemdc 13102 nninfself 13105 nninfsellemeq 13106 nninfsellemqall 13107 nninfsellemeqinf 13108 nninfomni 13111 nninffeq 13112 |
Copyright terms: Public domain | W3C validator |