Metamath Proof Explorer


Theorem resmptd

Description: Restriction of the mapping operation, deduction form. (Contributed by Glauco Siliprandi, 11-Dec-2019)

Ref Expression
Hypothesis resmptd.b ( 𝜑𝐵𝐴 )
Assertion resmptd ( 𝜑 → ( ( 𝑥𝐴𝐶 ) ↾ 𝐵 ) = ( 𝑥𝐵𝐶 ) )

Proof

Step Hyp Ref Expression
1 resmptd.b ( 𝜑𝐵𝐴 )
2 resmpt ( 𝐵𝐴 → ( ( 𝑥𝐴𝐶 ) ↾ 𝐵 ) = ( 𝑥𝐵𝐶 ) )
3 1 2 syl ( 𝜑 → ( ( 𝑥𝐴𝐶 ) ↾ 𝐵 ) = ( 𝑥𝐵𝐶 ) )