Theorem qseq1i

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

	Ref	Expression
Hypothesis	qseq1i.1	⊢ 𝐴 = 𝐵
Assertion	qseq1i	⊢ ( 𝐴 / 𝐶 ) = ( 𝐵 / 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		qseq1i.1	⊢ 𝐴 = 𝐵
2		qseq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 / 𝐶 ) = ( 𝐵 / 𝐶 ) )
3	1 2	ax-mp	⊢ ( 𝐴 / 𝐶 ) = ( 𝐵 / 𝐶 )