Theorem qseq2i 8709

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 8708	. 2 ⊢ (𝐴 = 𝐵 → (𝐶 / 𝐴) = (𝐶 / 𝐵))
3	1, 2	ax-mp 5	1 ⊢ (𝐶 / 𝐴) = (𝐶 / 𝐵)

Syntax hints:   = wceq 1542   / cqs 8646

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-rex 3063  df-rab 3402  df-v 3444  df-dif 3906  df-un 3908  df-in 3910  df-ss 3920  df-nul 4288  df-if 4482  df-sn 4583  df-pr 4585  df-op 4589  df-br 5101  df-opab 5163  df-cnv 5642  df-dm 5644  df-rn 5645  df-res 5646  df-ima 5647  df-ec 8649  df-qs 8653

This theorem is referenced by: (None)