Theorem qseq2i 8347

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 8346	. 2 ⊢ (𝐴 = 𝐵 → (𝐶 / 𝐴) = (𝐶 / 𝐵))
3	1, 2	ax-mp 5	1 ⊢ (𝐶 / 𝐴) = (𝐶 / 𝐵)

Syntax hints:   = wceq 1537   / cqs 8290

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-ext 2795

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1085  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-clab 2802  df-cleq 2816  df-clel 2895  df-nfc 2965  df-rex 3146  df-rab 3149  df-v 3498  df-dif 3941  df-un 3943  df-in 3945  df-ss 3954  df-nul 4294  df-if 4470  df-sn 4570  df-pr 4572  df-op 4576  df-br 5069  df-opab 5131  df-cnv 5565  df-dm 5567  df-rn 5568  df-res 5569  df-ima 5570  df-ec 8293  df-qs 8297

This theorem is referenced by:  prjspnval2  39274