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Mirrors > Home > ILE Home > Th. List > imaeq2i | GIF version |
Description: Equality theorem for image. (Contributed by NM, 21-Dec-2008.) |
Ref | Expression |
---|---|
imaeq1i.1 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
imaeq2i | ⊢ (𝐶 “ 𝐴) = (𝐶 “ 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imaeq1i.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | imaeq2 4765 | . 2 ⊢ (𝐴 = 𝐵 → (𝐶 “ 𝐴) = (𝐶 “ 𝐵)) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ (𝐶 “ 𝐴) = (𝐶 “ 𝐵) |
Colors of variables: wff set class |
Syntax hints: = wceq 1289 “ cima 4439 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-v 2621 df-un 3003 df-in 3005 df-ss 3012 df-sn 3450 df-pr 3451 df-op 3453 df-br 3844 df-opab 3898 df-xp 4442 df-cnv 4444 df-dm 4446 df-rn 4447 df-res 4448 df-ima 4449 |
This theorem is referenced by: cnvimarndm 4791 dmco 4934 fnimapr 5358 ssimaex 5359 imauni 5532 isoini2 5590 uniqs 6340 fiintim 6629 fidcenumlemrks 6652 fidcenumlemr 6654 nn0supp 8715 |
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