Description: Projection of a factor of an indexed Cartesian product. (Contributed by Glauco Siliprandi, 24-Dec-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | fvixp2 | ⊢ ( ( 𝐹 ∈ X 𝑥 ∈ 𝐴 𝐵 ∧ 𝑥 ∈ 𝐴 ) → ( 𝐹 ‘ 𝑥 ) ∈ 𝐵 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elixp2 | ⊢ ( 𝐹 ∈ X 𝑥 ∈ 𝐴 𝐵 ↔ ( 𝐹 ∈ V ∧ 𝐹 Fn 𝐴 ∧ ∀ 𝑥 ∈ 𝐴 ( 𝐹 ‘ 𝑥 ) ∈ 𝐵 ) ) | |
2 | 1 | simp3bi | ⊢ ( 𝐹 ∈ X 𝑥 ∈ 𝐴 𝐵 → ∀ 𝑥 ∈ 𝐴 ( 𝐹 ‘ 𝑥 ) ∈ 𝐵 ) |
3 | 2 | r19.21bi | ⊢ ( ( 𝐹 ∈ X 𝑥 ∈ 𝐴 𝐵 ∧ 𝑥 ∈ 𝐴 ) → ( 𝐹 ‘ 𝑥 ) ∈ 𝐵 ) |