Metamath Proof Explorer
Description: Slightly more general equality inference for the maps-to notation.
(Contributed by Glauco Siliprandi, 21-Dec-2024)
|
|
Ref |
Expression |
|
Hypotheses |
mpteq2dfa.1 |
⊢ Ⅎ 𝑥 𝜑 |
|
|
mpteq2dfa.2 |
⊢ ( ( 𝜑 ∧ 𝑥 ∈ 𝐴 ) → 𝐵 = 𝐶 ) |
|
Assertion |
mpteq2dfa |
⊢ ( 𝜑 → ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) = ( 𝑥 ∈ 𝐴 ↦ 𝐶 ) ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
mpteq2dfa.1 |
⊢ Ⅎ 𝑥 𝜑 |
2 |
|
mpteq2dfa.2 |
⊢ ( ( 𝜑 ∧ 𝑥 ∈ 𝐴 ) → 𝐵 = 𝐶 ) |
3 |
1 2
|
mpteq2da |
⊢ ( 𝜑 → ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) = ( 𝑥 ∈ 𝐴 ↦ 𝐶 ) ) |