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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 5901 | . 2 ⊢ (𝐴 = 𝐵 → (𝐶𝐴𝐷) = (𝐶𝐵𝐷)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝐶𝐴𝐷) = (𝐶𝐵𝐷) |
Colors of variables: wff set class |
Syntax hints: = wceq 1364 (class class class)co 5895 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-rex 2474 df-uni 3825 df-br 4019 df-iota 5196 df-fv 5243 df-ov 5898 |
This theorem is referenced by: oveq123i 5909 iseqvalcbv 10487 imasplusg 12782 mndprop 12899 issubm 12921 grpprop 12960 ablprop 13233 ringprop 13391 blres 14386 cncfmet 14531 |
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