Theorem qseq2i 8755

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 8754	. 2 ⊢ (𝐴 = 𝐵 → (𝐶 / 𝐴) = (𝐶 / 𝐵))
3	1, 2	ax-mp 5	1 ⊢ (𝐶 / 𝐴) = (𝐶 / 𝐵)

Syntax hints:   = wceq 1568   / cqs 8692

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-8 2143  ax-9 2151  ax-ext 2733

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1103  df-tru 1571  df-fal 1581  df-ex 1808  df-sb 2095  df-clab 2740  df-cleq 2753  df-clel 2836  df-rex 3088  df-rab 3415  df-v 3455  df-dif 3907  df-un 3909  df-in 3911  df-ss 3921  df-nul 4286  df-if 4487  df-sn 4589  df-pr 4591  df-op 4595  df-br 5109  df-opab 5173  df-cnv 5669  df-dm 5671  df-rn 5672  df-res 5673  df-ima 5674  df-ec 8695  df-qs 8699

This theorem is referenced by: (None)