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Theorem qseq2d 8706
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 8704 . 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 1542   / cqs 8648
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-rex 3075  df-rab 3409  df-v 3448  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4284  df-if 4488  df-sn 4588  df-pr 4590  df-op 4594  df-br 5107  df-opab 5169  df-cnv 5642  df-dm 5644  df-rn 5645  df-res 5646  df-ima 5647  df-ec 8651  df-qs 8655
This theorem is referenced by:  qustriv  32155  pstmval  32479  prjspnval2  40959  0prjspn  40969
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