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Mirrors > Home > ILE Home > Th. List > syl5ib | Unicode version |
Description: A mixed syllogism inference. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
syl5ib.1 | |
syl5ib.2 |
Ref | Expression |
---|---|
syl5ib |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl5ib.1 | . 2 | |
2 | syl5ib.2 | . . 3 | |
3 | 2 | biimpd 143 | . 2 |
4 | 1, 3 | syl5 32 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: syl5ibcom 154 syl5ibr 155 sbft 1820 gencl 2713 spsbc 2915 prexg 4128 posng 4606 sosng 4607 optocl 4610 relcnvexb 5073 funimass1 5195 dmfex 5307 f1ocnvb 5374 eqfnfv2 5512 elpreima 5532 dff13 5662 f1ocnvfv 5673 f1ocnvfvb 5674 fliftfun 5690 eusvobj2 5753 mpoxopn0yelv 6129 rntpos 6147 erexb 6447 findcard2 6776 findcard2s 6777 xpfi 6811 sbthlemi3 6840 enq0tr 7235 addnqprllem 7328 addnqprulem 7329 distrlem1prl 7383 distrlem1pru 7384 recexprlem1ssl 7434 recexprlem1ssu 7435 elrealeu 7630 addcan 7935 addcan2 7936 neg11 8006 negreb 8020 mulcanapd 8415 receuap 8423 cju 8712 nn1suc 8732 nnaddcl 8733 nndivtr 8755 znegclb 9080 zaddcllempos 9084 zmulcl 9100 zeo 9149 uz11 9341 uzp1 9352 eqreznegel 9399 xneg11 9610 xnegdi 9644 modqadd1 10127 modqmul1 10143 frec2uzltd 10169 bccmpl 10493 fz1eqb 10530 cj11 10670 rennim 10767 resqrexlemgt0 10785 efne0 11373 dvdsabseq 11534 uptx 12432 hmeocnvb 12476 tgioo 12704 bj-nnbidc 12951 bj-prexg 13098 strcollnft 13171 |
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