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Mirrors > Home > ILE Home > Th. List > oveqi | GIF version |
Description: Equality inference for operation value. (Contributed by NM, 24-Nov-2007.) |
Ref | Expression |
---|---|
oveq1i.1 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
oveqi | ⊢ (𝐶𝐴𝐷) = (𝐶𝐵𝐷) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq1i.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | oveq 5734 | . 2 ⊢ (𝐴 = 𝐵 → (𝐶𝐴𝐷) = (𝐶𝐵𝐷)) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ (𝐶𝐴𝐷) = (𝐶𝐵𝐷) |
Colors of variables: wff set class |
Syntax hints: = wceq 1314 (class class class)co 5728 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-rex 2396 df-uni 3703 df-br 3896 df-iota 5046 df-fv 5089 df-ov 5731 |
This theorem is referenced by: oveq123i 5742 iseqvalcbv 10123 blres 12423 cncfmet 12565 |
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