Theorem qseq2i

Description: Equality theorem for quotient set, inference form. (Contributed by Peter Mazsa, 3-Jun-2021)

	Ref	Expression
Hypothesis	qseq2i.1	⊢ 𝐴 = 𝐵
Assertion	qseq2i	⊢ ( 𝐶 / 𝐴 ) = ( 𝐶 / 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		qseq2i.1	⊢ 𝐴 = 𝐵
2		qseq2	⊢ ( 𝐴 = 𝐵 → ( 𝐶 / 𝐴 ) = ( 𝐶 / 𝐵 ) )
3	1 2	ax-mp	⊢ ( 𝐶 / 𝐴 ) = ( 𝐶 / 𝐵 )