Theorem qseq1i 39003

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 8760	. 2 ⊢ (𝐴 = 𝐵 → (𝐴 / 𝐶) = (𝐵 / 𝐶))
3	1, 2	ax-mp 5	1 ⊢ (𝐴 / 𝐶) = (𝐵 / 𝐶)

This proof depends on syntax axioms:   = wceq 1570   / cqs 8699

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-9 2156  ax-ext 2737

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-rex 3092  df-qs 8706

This theorem is used by:  dmqscoelseq  39453