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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 6673 | . 2 ⊢ (𝐹‘𝐴) = (𝐺‘𝐴) |
3 | fveq12i.2 | . . 3 ⊢ 𝐴 = 𝐵 | |
4 | 3 | fveq2i 6675 | . 2 ⊢ (𝐺‘𝐴) = (𝐺‘𝐵) |
5 | 2, 4 | eqtri 2846 | 1 ⊢ (𝐹‘𝐴) = (𝐺‘𝐵) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 ‘cfv 6357 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2795 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2802 df-cleq 2816 df-clel 2895 df-nfc 2965 df-rab 3149 df-v 3498 df-dif 3941 df-un 3943 df-in 3945 df-ss 3954 df-nul 4294 df-if 4470 df-sn 4570 df-pr 4572 df-op 4576 df-uni 4841 df-br 5069 df-iota 6316 df-fv 6365 |
This theorem is referenced by: cats1fvn 14222 sadcadd 15809 sadadd2 15811 coe1fzgsumdlem 20471 evl1gsumdlem 20521 madufval 21248 clwlkcompbp 27565 2wlkond 27718 1pthond 27925 3cycld 27959 2cycld 32387 kur14lem5 32459 bj-ndxarg 34370 fourierdlem62 42460 fouriersw 42523 |
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