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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 4885 | . 2 ⊢ (𝐴 = 𝐵 → (𝐶 “ 𝐴) = (𝐶 “ 𝐵)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝐶 “ 𝐴) = (𝐶 “ 𝐵) |
Colors of variables: wff set class |
Syntax hints: = wceq 1332 “ cima 4550 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-sn 3538 df-pr 3539 df-op 3541 df-br 3938 df-opab 3998 df-xp 4553 df-cnv 4555 df-dm 4557 df-rn 4558 df-res 4559 df-ima 4560 |
This theorem is referenced by: cnvimarndm 4911 dmco 5055 fnimapr 5489 ssimaex 5490 imauni 5670 isoini2 5728 uniqs 6495 fiintim 6825 fidcenumlemrks 6849 fidcenumlemr 6851 nn0supp 9053 ennnfonelem1 11956 ennnfonelemhf1o 11962 retopbas 12731 |
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