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Theorem qseq2d 8356
 Description: Equality theorem for quotient set, deduction form. (Contributed by Peter Mazsa, 27-May-2021.)
Hypothesis
Ref Expression
qseq2d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
qseq2d (𝜑 → (𝐶 / 𝐴) = (𝐶 / 𝐵))

Proof of Theorem qseq2d
StepHypRef Expression
1 qseq2d.1 . 2 (𝜑𝐴 = 𝐵)
2 qseq2 8354 . 2 (𝐴 = 𝐵 → (𝐶 / 𝐴) = (𝐶 / 𝐵))
31, 2syl 17 1 (𝜑 → (𝐶 / 𝐴) = (𝐶 / 𝐵))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1538   / cqs 8298 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 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2729 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2736  df-cleq 2750  df-clel 2830  df-rex 3076  df-rab 3079  df-v 3411  df-un 3863  df-in 3865  df-ss 3875  df-sn 4523  df-pr 4525  df-op 4529  df-br 5033  df-opab 5095  df-cnv 5532  df-dm 5534  df-rn 5535  df-res 5536  df-ima 5537  df-ec 8301  df-qs 8305 This theorem is referenced by:  qustriv  31081  prjspnval2  39976  0prjspn  39984
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