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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 338 | 1 ⊢ ((𝜒 ∧ 𝜑) → (𝜒 ∧ 𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 |
This theorem is referenced by: sylanl2 403 sylanr2 405 andi 818 pm4.55dc 938 xoranor 1377 19.41h 1685 sbimi 1764 equs5e 1795 exdistrfor 1800 equs45f 1802 sbidm 1851 eu3h 2071 eupickb 2107 2exeu 2118 darii 2126 festino 2132 baroco 2133 r19.27v 2604 r19.27av 2612 rspc2ev 2857 reu3 2928 difdif 3261 ssddif 3370 inssdif 3372 difin 3373 difindiss 3390 indifdir 3392 difrab 3410 iundif2ss 3953 trssord 4381 ordsuc 4563 find 4599 imainss 5045 dffun5r 5229 fof 5439 f1ocnv 5475 fv3 5539 relelfvdm 5548 funimass4 5567 fvelimab 5573 funconstss 5635 dff2 5661 dffo5 5666 dff1o6 5777 oprabid 5907 ssoprab2i 5964 releldm2 6186 ixpf 6720 recexgt0sr 7772 map2psrprg 7804 lediv2a 8852 lbreu 8902 elfzp12 10099 fihashf1rn 10768 cau3lem 11123 fsumcl2lem 11406 dvdsnegb 11815 dvds2add 11832 dvds2sub 11833 ndvdssub 11935 gcd2n0cl 11970 divgcdcoprmex 12102 cncongr1 12103 ctinfom 12429 istopfin 13503 toponcom 13530 cnptoprest 13742 |
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