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Mirrors > Home > MPE Home > Th. List > orcomd | Structured version Visualization version GIF version |
Description: Commutation of disjuncts in consequent. (Contributed by NM, 2-Dec-2010.) |
Ref | Expression |
---|---|
orcomd.1 | ⊢ (𝜑 → (𝜓 ∨ 𝜒)) |
Ref | Expression |
---|---|
orcomd | ⊢ (𝜑 → (𝜒 ∨ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orcomd.1 | . 2 ⊢ (𝜑 → (𝜓 ∨ 𝜒)) | |
2 | orcom 401 | . 2 ⊢ ((𝜓 ∨ 𝜒) ↔ (𝜒 ∨ 𝜓)) | |
3 | 1, 2 | sylib 207 | 1 ⊢ (𝜑 → (𝜒 ∨ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∨ wo 382 |
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 df-or 384 |
This theorem is referenced by: olcd 407 19.33b 1802 swopo 4969 fr2nr 5016 ordtri1 5673 ordequn 5745 ssonprc 6884 ordunpr 6918 ordunisuc2 6936 2oconcl 7470 erdisj 7681 ordtypelem7 8312 ackbij1lem18 8942 fin23lem19 9041 gchi 9325 inar1 9476 inatsk 9479 avgle 11151 nnm1nn0 11211 uzsplit 12281 fzospliti 12369 fzouzsplit 12372 fz1f1o 14288 odcl 17778 gexcl 17818 lssvs0or 18931 lspdisj 18946 lspsncv0 18967 mdetralt 20233 filcon 21497 limccnp 23461 dgrlt 23826 logreclem 24300 atans2 24458 basellem3 24609 sqff1o 24708 tgcgrsub2 25290 legov3 25293 colline 25344 tglowdim2ln 25346 mirbtwnhl 25375 colmid 25383 symquadlem 25384 midexlem 25387 ragperp 25412 colperp 25421 midex 25429 oppperpex 25445 hlpasch 25448 colopp 25461 colhp 25462 lmieu 25476 lmicom 25480 lmimid 25486 lmiisolem 25488 trgcopy 25496 cgracgr 25510 cgraswap 25512 cgracol 25519 hashecclwwlkn1 26361 znsqcld 28900 xlt2addrd 28913 esumcvgre 29480 eulerpartlemgvv 29765 nobndup 31099 ordtoplem 31604 ordcmp 31616 onsucuni3 32391 dvasin 32666 unitresr 33055 lkrshp4 33413 2at0mat0 33829 trlator0 34476 dia2dimlem2 35372 dia2dimlem3 35373 dochkrshp 35693 dochkrshp4 35696 lcfl6 35807 lclkrlem2k 35824 hdmap14lem6 36183 hgmapval0 36202 acongneg2 36562 unxpwdom3 36683 elunnel2 38221 disjinfi 38375 xrssre 38505 icccncfext 38773 wallispilem3 38960 fourierdlem93 39092 fourierdlem101 39100 hashecclwwlksn1 41261 nneop 42114 |
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