Theorem qseq1i 38275

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 8738	. 2 ⊢ (𝐴 = 𝐵 → (𝐴 / 𝐶) = (𝐵 / 𝐶))
3	1, 2	ax-mp 5	1 ⊢ (𝐴 / 𝐶) = (𝐵 / 𝐶)

Syntax hints:   = wceq 1540   / cqs 8681

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-9 2119  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-rex 3056  df-qs 8688

This theorem is referenced by:  dmqscoelseq  38646