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Mirrors > Home > MPE Home > Th. List > anim1d | Structured version Visualization version GIF version |
Description: Add a conjunct to right of antecedent and consequent in a deduction. (Contributed by NM, 3-Apr-1994.) |
Ref | Expression |
---|---|
anim1d.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
anim1d | ⊢ (𝜑 → ((𝜓 ∧ 𝜃) → (𝜒 ∧ 𝜃))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anim1d.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | idd 24 | . 2 ⊢ (𝜑 → (𝜃 → 𝜃)) | |
3 | 1, 2 | anim12d 609 | 1 ⊢ (𝜑 → ((𝜓 ∧ 𝜃) → (𝜒 ∧ 𝜃))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 395 |
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 |
This theorem is referenced by: pm3.45 622 exdistrf 2450 2ax6elem 2473 mopick2 2635 ssrexf 4062 ssrexvOLD 4069 ssdif 4154 ssrin 4250 reupick 4335 disjss1 5121 copsexgw 5501 copsexg 5502 propeqop 5517 po3nr 5612 frss 5653 coss2 5870 ordsssuc2 6477 fununi 6643 dffv2 7004 oprabidw 7462 poseq 8182 extmptsuppeq 8212 onfununi 8380 oaass 8598 ssnnfi 9208 fiint 9364 fiintOLD 9365 fiss 9462 wemapsolem 9588 tcss 9782 ac6s 10522 reclem2pr 11086 qbtwnxr 13239 ico0 13430 icoshft 13510 2ffzeq 13686 clsslem 15020 r19.2uz 15387 isprm7 16742 prmdvdsncoprmbd 16761 infpn2 16947 prmgaplem4 17088 fthres2 17986 ablfacrplem 20100 rnglidlmmgm 21273 psdmul 22188 monmat2matmon 22846 neiss 23133 uptx 23649 txcn 23650 nrmr0reg 23773 cnpflfi 24023 cnextcn 24091 caussi 25345 ovolsslem 25533 tgtrisegint 28522 inagswap 28864 shorth 31324 mptssALT 32692 uzssico 32793 zarclsint 33833 ordtconnlem1 33885 omsmon 34280 omssubadd 34282 subgrtrl 35118 subgrcycl 35120 acycgrsubgr 35143 mclsax 35554 trisegint 36010 segcon2 36087 opnrebl2 36304 bj-19.42t 36756 poimirlem30 37637 itg2addnclem 37658 itg2addnclem2 37659 fdc1 37733 totbndss 37764 ablo4pnp 37867 keridl 38019 dib2dim 41226 dih2dimbALTN 41228 dvh1dim 41425 mapdpglem2 41656 pell14qrss1234 42844 pell1qrss14 42856 rmxycomplete 42906 lnr2i 43105 fzunt 43445 fzuntd 43446 fzunt1d 43447 fzuntgd 43448 rp-fakeanorass 43503 rfcnnnub 44974 or2expropbi 46984 2ffzoeq 47277 ich2exprop 47396 nnsum4primes4 47714 nnsum4primesprm 47716 nnsum4primesgbe 47718 nnsum4primesle9 47720 opnneir 48703 |
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