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Mirrors > Home > ILE Home > Th. List > fveq12i | GIF version |
Description: Equality deduction for function value. (Contributed by FL, 27-Jun-2014.) |
Ref | Expression |
---|---|
fveq12i.1 | ⊢ 𝐹 = 𝐺 |
fveq12i.2 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
fveq12i | ⊢ (𝐹‘𝐴) = (𝐺‘𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveq12i.1 | . . 3 ⊢ 𝐹 = 𝐺 | |
2 | 1 | fveq1i 5199 | . 2 ⊢ (𝐹‘𝐴) = (𝐺‘𝐴) |
3 | fveq12i.2 | . . 3 ⊢ 𝐴 = 𝐵 | |
4 | 3 | fveq2i 5201 | . 2 ⊢ (𝐺‘𝐴) = (𝐺‘𝐵) |
5 | 2, 4 | eqtri 2101 | 1 ⊢ (𝐹‘𝐴) = (𝐺‘𝐵) |
Colors of variables: wff set class |
Syntax hints: = wceq 1284 ‘cfv 4922 |
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 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rex 2354 df-v 2603 df-un 2977 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-iota 4887 df-fv 4930 |
This theorem is referenced by: (None) |
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