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Mirrors > Home > ILE Home > Th. List > anim2i | GIF version |
Description: Introduce conjunct to both sides of an implication. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
anim1i.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
anim2i | ⊢ ((𝜒 ∧ 𝜑) → (𝜒 ∧ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 ⊢ (𝜒 → 𝜒) | |
2 | anim1i.1 | . 2 ⊢ (𝜑 → 𝜓) | |
3 | 1, 2 | anim12i 336 | 1 ⊢ ((𝜒 ∧ 𝜑) → (𝜒 ∧ 𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem is referenced by: sylanl2 400 sylanr2 402 andi 807 pm4.55dc 922 xoranor 1355 19.41h 1663 sbimi 1737 equs5e 1767 exdistrfor 1772 equs45f 1774 sbidm 1823 eu3h 2042 eupickb 2078 2exeu 2089 darii 2097 festino 2103 baroco 2104 r19.27v 2557 r19.27av 2565 rspc2ev 2799 reu3 2869 difdif 3196 ssddif 3305 inssdif 3307 difin 3308 difindiss 3325 indifdir 3327 difrab 3345 iundif2ss 3873 trssord 4297 ordsuc 4473 find 4508 imainss 4949 dffun5r 5130 fof 5340 f1ocnv 5373 fv3 5437 relelfvdm 5446 funimass4 5465 fvelimab 5470 funconstss 5531 dff2 5557 dffo5 5562 dff1o6 5670 oprabid 5796 ssoprab2i 5853 releldm2 6076 ixpf 6607 recexgt0sr 7574 map2psrprg 7606 lediv2a 8646 lbreu 8696 elfzp12 9872 focdmex 10526 fihashf1rn 10528 cau3lem 10879 fsumcl2lem 11160 dvdsnegb 11499 dvds2add 11516 dvds2sub 11517 ndvdssub 11616 gcd2n0cl 11647 divgcdcoprmex 11772 cncongr1 11773 ctinfom 11930 istopfin 12156 toponcom 12183 cnptoprest 12397 |
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