Theorem qseq1i 38225

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

Hypothesis

Ref	Expression
qseq1i.1	⊢ 𝐴 = 𝐵

Assertion

Ref	Expression
qseq1i	⊢ (𝐴 / 𝐶) = (𝐵 / 𝐶)

Proof of Theorem qseq1i

Step	Hyp	Ref	Expression
1		qseq1i.1	. 2 ⊢ 𝐴 = 𝐵
2		qseq1 8782	. 2 ⊢ (𝐴 = 𝐵 → (𝐴 / 𝐶) = (𝐵 / 𝐶))
3	1, 2	ax-mp 5	1 ⊢ (𝐴 / 𝐶) = (𝐵 / 𝐶)

Syntax hints:   = wceq 1539   / cqs 8725

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-9 2117  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1779  df-sb 2064  df-clab 2713  df-cleq 2726  df-rex 3060  df-qs 8732

This theorem is referenced by:  dmqscoelseq  38596