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Mirrors > Home > MPE Home > Th. List > 3comr | Structured version Visualization version GIF version |
Description: Commutation in antecedent. Rotate right. (Contributed by NM, 28-Jan-1996.) (Revised by Wolf Lammen, 9-Apr-2022.) |
Ref | Expression |
---|---|
3exp.1 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
3comr | ⊢ ((𝜒 ∧ 𝜑 ∧ 𝜓) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3exp.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) | |
2 | 1 | 3com12 1122 | . 2 ⊢ ((𝜓 ∧ 𝜑 ∧ 𝜒) → 𝜃) |
3 | 2 | 3com13 1123 | 1 ⊢ ((𝜒 ∧ 𝜑 ∧ 𝜓) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1086 |
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 207 df-an 396 df-3an 1088 |
This theorem is referenced by: 3com23 1125 sbciegft 3828 oacan 8584 omlimcl 8614 nnacan 8664 dif1en 9198 dif1enOLD 9200 unfi 9209 en3lplem2 9650 le2tri3i 11388 ltaddsublt 11887 div12 11941 lemul12b 12121 zdivadd 12686 zdivmul 12687 elfz 13549 fzmmmeqm 13593 fzrev 13623 modmulnn 13925 digit2 14271 digit1 14272 faclbnd5 14333 hashfundm 14477 absdiflt 15352 absdifle 15353 dvds0lem 16300 dvdsmulc 16317 dvds2add 16323 dvds2sub 16324 dvdstr 16327 lcmdvds 16641 pospropd 18384 fmfil 23967 elfm 23970 psmettri2 24334 xmettri2 24365 stdbdmetval 24542 nmf2 24621 isclmi0 25144 iscvsi 25175 brbtwn 28928 colinearalglem3 28937 colinearalg 28939 isvciOLD 30608 nvtri 30698 nmooge0 30795 his7 31118 his2sub2 31121 braadd 31973 bramul 31974 cnlnadjlem2 32096 pjimai 32204 atcvati 32414 mdsymlem5 32435 bnj240 34691 bnj1189 35001 cusgredgex 35105 colineardim1 36042 ftc1anclem6 37684 brcnvrabga 38323 oaord3 43281 omord2com 43291 uun123p3 44808 stoweidlem2 45957 sigarperm 46815 leaddsuble 47246 |
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