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Mirrors > Home > MPE Home > Th. List > bitr2d | Structured version Visualization version GIF version |
Description: Deduction form of bitr2i 264. (Contributed by NM, 9-Jun-2004.) |
Ref | Expression |
---|---|
bitr2d.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
bitr2d.2 | ⊢ (𝜑 → (𝜒 ↔ 𝜃)) |
Ref | Expression |
---|---|
bitr2d | ⊢ (𝜑 → (𝜃 ↔ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bitr2d.1 | . . 3 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
2 | bitr2d.2 | . . 3 ⊢ (𝜑 → (𝜒 ↔ 𝜃)) | |
3 | 1, 2 | bitrd 267 | . 2 ⊢ (𝜑 → (𝜓 ↔ 𝜃)) |
4 | 3 | bicomd 212 | 1 ⊢ (𝜑 → (𝜃 ↔ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 195 |
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 196 |
This theorem is referenced by: 3bitrrd 294 3bitr2rd 296 pm5.18 370 ifptru 1017 sbequ12a 2099 elrnmpt1 5295 fndmdif 6229 weniso 6504 sbcopeq1a 7111 cfss 8970 posdif 10400 lesub1 10401 lesub0 10424 possumd 10531 ltdivmul 10777 ledivmul 10778 zlem1lt 11306 zltlem1 11307 negelrp 11740 ioon0 12072 fzn 12228 fzrev2 12274 fz1sbc 12285 elfzp1b 12286 sumsqeq0 12804 fz1isolem 13102 sqrtle 13849 absgt0 13912 isershft 14242 incexc2 14409 dvdssubr 14865 gcdn0gt0 15077 divgcdcoprmex 15218 pcfac 15441 ramval 15550 ltbwe 19293 iunocv 19844 lmbrf 20874 perfcls 20979 ovolscalem1 23088 itg2mulclem 23319 sineq0 24077 efif1olem4 24095 atanord 24454 rlimcnp2 24493 bposlem7 24815 lgsprme0 24864 rpvmasum2 25001 trgcgrg 25210 legov3 25293 opphllem6 25444 ebtwntg 25662 wwlkm1edg 26263 usg2spthonot0 26416 hial2eq2 27348 adjsym 28076 cnvadj 28135 eigvalcl 28204 mddmd 28544 mdslmd2i 28573 elat2 28583 xdivpnfrp 28972 isorng 29130 unitdivcld 29275 indpreima 29414 iooscon 30483 pdivsq 30888 poimirlem26 32605 areacirclem1 32670 isat3 33612 ishlat3N 33659 cvrval5 33719 llnexchb2 34173 lhpoc2N 34319 lhprelat3N 34344 lautcnvle 34393 lautcvr 34396 ltrncnvatb 34442 cdlemb3 34912 cdlemg17h 34974 dih0vbN 35589 djhcvat42 35722 dvh4dimat 35745 mapdordlem2 35944 diophun 36355 jm2.19lem4 36577 uneqsn 37341 xrralrecnnge 38554 flsqrt5 40047 wwlksm1edg 41078 isrnghm 41682 lincfsuppcl 41996 logge0b 42123 loggt0b 42124 logle1b 42125 loglt1b 42126 |
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