Theorem qseq2i 8489

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

Hypothesis

Ref	Expression
qseq2i.1	⊢ 𝐴 = 𝐵

Assertion

Ref	Expression
qseq2i	⊢ (𝐶 / 𝐴) = (𝐶 / 𝐵)

Proof of Theorem qseq2i

Step	Hyp	Ref	Expression
1		qseq2i.1	. 2 ⊢ 𝐴 = 𝐵
2		qseq2 8488	. 2 ⊢ (𝐴 = 𝐵 → (𝐶 / 𝐴) = (𝐶 / 𝐵))
3	1, 2	ax-mp 5	1 ⊢ (𝐶 / 𝐴) = (𝐶 / 𝐵)

Syntax hints:   = wceq 1543   / cqs 8432

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2114  ax-9 2122  ax-ext 2710

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-3an 1091  df-tru 1546  df-fal 1556  df-ex 1788  df-sb 2073  df-clab 2717  df-cleq 2731  df-clel 2818  df-rex 3070  df-rab 3073  df-v 3425  df-dif 3887  df-un 3889  df-in 3891  df-ss 3901  df-nul 4255  df-if 4457  df-sn 4559  df-pr 4561  df-op 4565  df-br 5071  df-opab 5133  df-cnv 5587  df-dm 5589  df-rn 5590  df-res 5591  df-ima 5592  df-ec 8435  df-qs 8439

This theorem is referenced by: (None)