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Mirrors > Home > ILE Home > Th. List > imaeq2d | GIF version |
Description: Equality theorem for image. (Contributed by FL, 15-Dec-2006.) |
Ref | Expression |
---|---|
imaeq1d.1 | ⊢ (φ → A = B) |
Ref | Expression |
---|---|
imaeq2d | ⊢ (φ → (𝐶 “ A) = (𝐶 “ B)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imaeq1d.1 | . 2 ⊢ (φ → A = B) | |
2 | imaeq2 4607 | . 2 ⊢ (A = B → (𝐶 “ A) = (𝐶 “ B)) | |
3 | 1, 2 | syl 14 | 1 ⊢ (φ → (𝐶 “ A) = (𝐶 “ B)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 = wceq 1242 “ cima 4291 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-v 2553 df-un 2916 df-in 2918 df-ss 2925 df-sn 3373 df-pr 3374 df-op 3376 df-br 3756 df-opab 3810 df-xp 4294 df-cnv 4296 df-dm 4298 df-rn 4299 df-res 4300 df-ima 4301 |
This theorem is referenced by: imaeq12d 4612 nfimad 4620 elimasng 4636 ressn 4801 foima 5054 f1imacnv 5086 fvco2 5185 fsn2 5280 resfunexg 5325 funfvima3 5335 funiunfvdm 5345 isoselem 5402 fnexALT 5682 eceq1 6077 uniqs2 6102 ecinxp 6117 |
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