Theorem reseq12i

Description: Equality inference for restrictions. (Contributed by NM, 21-Oct-2014)

	Ref	Expression
Hypotheses	reseqi.1	⊢ 𝐴 = 𝐵
	reseqi.2	⊢ 𝐶 = 𝐷
Assertion	reseq12i	⊢ ( 𝐴 ↾ 𝐶 ) = ( 𝐵 ↾ 𝐷 )

Proof

Step	Hyp	Ref	Expression
1		reseqi.1	⊢ 𝐴 = 𝐵
2		reseqi.2	⊢ 𝐶 = 𝐷
3	1	reseq1i	⊢ ( 𝐴 ↾ 𝐶 ) = ( 𝐵 ↾ 𝐶 )
4	2	reseq2i	⊢ ( 𝐵 ↾ 𝐶 ) = ( 𝐵 ↾ 𝐷 )
5	3 4	eqtri	⊢ ( 𝐴 ↾ 𝐶 ) = ( 𝐵 ↾ 𝐷 )