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Mirrors > Home > ILE Home > Th. List > 3imtr4d | Unicode version |
Description: More general version of 3imtr4i 201. Useful for converting conditional definitions in a formula. (Contributed by NM, 26-Oct-1995.) |
Ref | Expression |
---|---|
3imtr4d.1 |
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3imtr4d.2 |
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3imtr4d.3 |
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Ref | Expression |
---|---|
3imtr4d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3imtr4d.2 |
. 2
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2 | 3imtr4d.1 |
. . 3
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3 | 3imtr4d.3 |
. . 3
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4 | 2, 3 | sylibrd 169 |
. 2
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5 | 1, 4 | sylbid 150 |
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 106 ax-ia2 107 ax-ia3 108 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: onsucelsucr 4508 unielrel 5157 ovmpos 5998 caofrss 6107 caoftrn 6108 f1o2ndf1 6229 nnaord 6510 nnmord 6518 oviec 6641 pmss12g 6675 fiss 6976 pm54.43 7189 ltsopi 7319 lttrsr 7761 ltsosr 7763 aptisr 7778 mulextsr1 7780 axpre-mulext 7887 axltwlin 8025 axlttrn 8026 axltadd 8027 axmulgt0 8029 letr 8040 eqord1 8440 remulext1 8556 mulext1 8569 recexap 8610 prodge0 8811 lt2msq 8843 nnge1 8942 zltp1le 9307 uzss 9548 eluzp1m1 9551 xrletr 9808 ixxssixx 9902 zesq 10639 expcanlem 10695 expcan 10696 nn0opthd 10702 maxleast 11222 climshftlemg 11310 dvds1lem 11809 bezoutlemzz 12003 algcvg 12048 eucalgcvga 12058 rpexp12i 12155 crth 12224 pc2dvds 12329 pcmpt 12341 prmpwdvds 12353 1arith 12365 ercpbl 12750 insubm 12872 subginv 13041 dvdsunit 13281 subrgdvds 13356 tgss 13566 neipsm 13657 ssrest 13685 cos11 14277 lgsdir2lem4 14435 m1lgs 14455 |
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