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Mirrors > Home > MPE Home > Th. List > fveq12i | Structured version Visualization version 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 6104 | . 2 ⊢ (𝐹‘𝐴) = (𝐺‘𝐴) |
3 | fveq12i.2 | . . 3 ⊢ 𝐴 = 𝐵 | |
4 | 3 | fveq2i 6106 | . 2 ⊢ (𝐺‘𝐴) = (𝐺‘𝐵) |
5 | 2, 4 | eqtri 2632 | 1 ⊢ (𝐹‘𝐴) = (𝐺‘𝐵) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1475 ‘cfv 5804 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-3an 1033 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-rex 2902 df-rab 2905 df-v 3175 df-dif 3543 df-un 3545 df-in 3547 df-ss 3554 df-nul 3875 df-if 4037 df-sn 4126 df-pr 4128 df-op 4132 df-uni 4373 df-br 4584 df-iota 5768 df-fv 5812 |
This theorem is referenced by: cats1fvn 13454 sadcadd 15018 sadadd2 15020 coe1fzgsumdlem 19492 evl1gsumdlem 19541 madufval 20262 kur14lem5 30446 fourierdlem62 39061 fouriersw 39124 21wlkond 41144 1pthond 41311 3cycld 41345 |
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