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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 1121 | . 2 ⊢ ((𝜓 ∧ 𝜑 ∧ 𝜒) → 𝜃) |
3 | 2 | 3com13 1122 | 1 ⊢ ((𝜒 ∧ 𝜑 ∧ 𝜓) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1085 |
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 206 df-an 395 df-3an 1087 |
This theorem is referenced by: 3com23 1124 oacan 8552 omlimcl 8582 nnacan 8632 dif1en 9164 dif1enOLD 9166 unfi 9176 en3lplem2 9612 le2tri3i 11350 ltaddsublt 11847 div12 11900 lemul12b 12077 zdivadd 12639 zdivmul 12640 elfz 13496 fzmmmeqm 13540 fzrev 13570 modmulnn 13860 digit2 14205 digit1 14206 faclbnd5 14264 hashfundm 14408 absdiflt 15270 absdifle 15271 dvds0lem 16216 dvdsmulc 16233 dvds2add 16239 dvds2sub 16240 dvdstr 16243 lcmdvds 16551 pospropd 18286 fmfil 23670 elfm 23673 psmettri2 24037 xmettri2 24068 stdbdmetval 24245 nmf2 24324 isclmi0 24847 iscvsi 24878 brbtwn 28422 colinearalglem3 28431 colinearalg 28433 isvciOLD 30098 nvtri 30188 nmooge0 30285 his7 30608 his2sub2 30611 braadd 31463 bramul 31464 cnlnadjlem2 31586 pjimai 31694 atcvati 31904 mdsymlem5 31925 bnj240 34006 bnj1189 34316 cusgredgex 34408 colineardim1 35335 ftc1anclem6 36871 brcnvrabga 37516 oaord3 42346 omord2com 42356 uun123p3 43876 stoweidlem2 45018 sigarperm 45876 leaddsuble 46305 |
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