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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 |
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Ref | Expression |
---|---|
ifbid |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ifbid.1 |
. 2
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2 | ifbi 3497 |
. 2
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3 | 1, 2 | syl 14 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
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 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-11 1485 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-if 3480 |
This theorem is referenced by: ifbieq1d 3499 ifbieq2d 3501 ifbieq12d 3503 ifandc 3513 fodjum 7026 fodju0 7027 fodjuomni 7029 nnnninf 7031 fodjumkv 7042 xaddval 9658 0tonninf 10243 1tonninf 10244 sumeq1 11156 summodc 11184 zsumdc 11185 fsum3 11188 isumss 11192 sumsplitdc 11233 prodeq1f 11353 zproddc 11380 fprodseq 11384 subctctexmid 13369 nninfalllemn 13377 nninfalllem1 13378 nninfsellemdc 13381 nninfself 13384 nninfsellemeq 13385 nninfsellemqall 13386 nninfsellemeqinf 13387 nninfomni 13390 nninffeq 13391 dceqnconst 13423 |
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