![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > oveqd | GIF version |
Description: Equality deduction for operation value. (Contributed by NM, 9-Sep-2006.) |
Ref | Expression |
---|---|
oveq1d.1 | ⊢ (φ → A = B) |
Ref | Expression |
---|---|
oveqd | ⊢ (φ → (𝐶A𝐷) = (𝐶B𝐷)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq1d.1 | . 2 ⊢ (φ → A = B) | |
2 | oveq 5461 | . 2 ⊢ (A = B → (𝐶A𝐷) = (𝐶B𝐷)) | |
3 | 1, 2 | syl 14 | 1 ⊢ (φ → (𝐶A𝐷) = (𝐶B𝐷)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 = wceq 1242 (class class class)co 5455 |
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-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-rex 2306 df-uni 3572 df-br 3756 df-iota 4810 df-fv 4853 df-ov 5458 |
This theorem is referenced by: oveq123d 5476 csbov12g 5486 ovmpt2dxf 5568 oprssov 5584 ofeq 5656 iseqeq2 8895 |
Copyright terms: Public domain | W3C validator |