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Mirrors > Home > MPE Home > Th. List > fvmpt2 | Structured version Visualization version GIF version |
Description: Value of a function given by the maps-to notation. (Contributed by FL, 21-Jun-2010.) |
Ref | Expression |
---|---|
mptrcl.1 | ⊢ 𝐹 = (𝑥 ∈ 𝐴 ↦ 𝐵) |
Ref | Expression |
---|---|
fvmpt2 | ⊢ ((𝑥 ∈ 𝐴 ∧ 𝐵 ∈ 𝐶) → (𝐹‘𝑥) = 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mptrcl.1 | . . 3 ⊢ 𝐹 = (𝑥 ∈ 𝐴 ↦ 𝐵) | |
2 | 1 | fvmpt2i 6847 | . 2 ⊢ (𝑥 ∈ 𝐴 → (𝐹‘𝑥) = ( I ‘𝐵)) |
3 | fvi 6806 | . 2 ⊢ (𝐵 ∈ 𝐶 → ( I ‘𝐵) = 𝐵) | |
4 | 2, 3 | sylan9eq 2799 | 1 ⊢ ((𝑥 ∈ 𝐴 ∧ 𝐵 ∈ 𝐶) → (𝐹‘𝑥) = 𝐵) |
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