Metamath Proof Explorer


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 𝑥 𝜑
mpteq2dfa.2 ( ( 𝜑𝑥𝐴 ) → 𝐵 = 𝐶 )
Assertion mpteq2dfa ( 𝜑 → ( 𝑥𝐴𝐵 ) = ( 𝑥𝐴𝐶 ) )

Proof

Step Hyp Ref Expression
1 mpteq2dfa.1 𝑥 𝜑
2 mpteq2dfa.2 ( ( 𝜑𝑥𝐴 ) → 𝐵 = 𝐶 )
3 1 2 mpteq2da ( 𝜑 → ( 𝑥𝐴𝐵 ) = ( 𝑥𝐴𝐶 ) )