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Mirrors > Home > MPE Home > Th. List > fveq12d | Structured version Visualization version GIF version |
Description: Equality deduction for function value. (Contributed by FL, 22-Dec-2008.) |
Ref | Expression |
---|---|
fveq12d.1 | ⊢ (𝜑 → 𝐹 = 𝐺) |
fveq12d.2 | ⊢ (𝜑 → 𝐴 = 𝐵) |
Ref | Expression |
---|---|
fveq12d | ⊢ (𝜑 → (𝐹‘𝐴) = (𝐺‘𝐵)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveq12d.1 | . . 3 ⊢ (𝜑 → 𝐹 = 𝐺) | |
2 | 1 | fveq1d 6719 | . 2 ⊢ (𝜑 → (𝐹‘𝐴) = (𝐺‘𝐴)) |
3 | fveq12d.2 | . . 3 ⊢ (𝜑 → 𝐴 = 𝐵) | |
4 | 3 | fveq2d 6721 | . 2 ⊢ (𝜑 → (𝐺‘𝐴) = (𝐺‘𝐵)) |
5 | 2, 4 | eqtrd 2777 | 1 ⊢ (𝜑 → (𝐹‘𝐴) = (𝐺‘𝐵)) |
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