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Theorem qseq1d 8803
Description: Equality theorem for quotient set, deduction form. (Contributed by Peter Mazsa, 27-May-2021.)
Hypothesis
Ref Expression
qseq1d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
qseq1d (𝜑 → (𝐴 / 𝐶) = (𝐵 / 𝐶))

Proof of Theorem qseq1d
StepHypRef Expression
1 qseq1d.1 . 2 (𝜑𝐴 = 𝐵)
2 qseq1 8800 . 2 (𝐴 = 𝐵 → (𝐴 / 𝐶) = (𝐵 / 𝐶))
31, 2syl 17 1 (𝜑 → (𝐴 / 𝐶) = (𝐵 / 𝐶))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1537   / cqs 8743
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-rex 3069  df-qs 8750
This theorem is referenced by:  fracbas  33287  n0elim  38632
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