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Mirrors > Home > MPE Home > Th. List > fveq1d | Structured version Visualization version GIF version |
Description: Equality deduction for function value. (Contributed by NM, 2-Sep-2003.) |
Ref | Expression |
---|---|
fveq1d.1 | ⊢ (𝜑 → 𝐹 = 𝐺) |
Ref | Expression |
---|---|
fveq1d | ⊢ (𝜑 → (𝐹‘𝐴) = (𝐺‘𝐴)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveq1d.1 | . 2 ⊢ (𝜑 → 𝐹 = 𝐺) | |
2 | fveq1 6738 | . 2 ⊢ (𝐹 = 𝐺 → (𝐹‘𝐴) = (𝐺‘𝐴)) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝐹‘𝐴) = (𝐺‘𝐴)) |
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