Description: Bound-variable hypothesis builder for mapping, special case. (Contributed by Mario Carneiro, 25-Dec-2016)
Ref | Expression | ||
---|---|---|---|
Assertion | nffvmpt1 | ⊢ Ⅎ 𝑥 ( ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) ‘ 𝐶 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfmpt1 | ⊢ Ⅎ 𝑥 ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) | |
2 | nfcv | ⊢ Ⅎ 𝑥 𝐶 | |
3 | 1 2 | nffv | ⊢ Ⅎ 𝑥 ( ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) ‘ 𝐶 ) |