Metamath Proof Explorer


Theorem reseq2i

Description: Equality inference for restrictions. (Contributed by Paul Chapman, 22-Jun-2011)

Ref Expression
Hypothesis reseqi.1 ⊢ 𝐴 = 𝐵
Assertion reseq2i ( 𝐶 ↾ 𝐴 ) = ( 𝐶 ↾ 𝐵 )

Proof

Step Hyp Ref Expression
1 reseqi.1 ⊢ 𝐴 = 𝐵
2 reseq2 ⊢ ( 𝐴 = 𝐵 → ( 𝐶 ↾ 𝐴 ) = ( 𝐶 ↾ 𝐵 ) )
3 1 2 ax-mp ⊢ ( 𝐶 ↾ 𝐴 ) = ( 𝐶 ↾ 𝐵 )