Theorem mpteq2dfa

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 ) )