Theorem qseq1d

Description: Equality theorem for quotient set, deduction form. (Contributed by Peter Mazsa, 27-May-2021)

	Ref	Expression
Hypothesis	qseq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	qseq1d	⊢ ( 𝜑 → ( 𝐴 / 𝐶 ) = ( 𝐵 / 𝐶 ) )

Proof

Step	Hyp	Ref	Expression
1		qseq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		qseq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 / 𝐶 ) = ( 𝐵 / 𝐶 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 / 𝐶 ) = ( 𝐵 / 𝐶 ) )