Theorem dmqseqi 39860

Description: Equality theorem for domain quotient, inference version. (Contributed by Peter Mazsa, 26-Sep-2021.)

Hypothesis

Ref	Expression
dmqseqi.1	⊢ 𝑅 = 𝑆

Assertion

Ref	Expression
dmqseqi	⊢ (dom 𝑅 / 𝑅) = (dom 𝑆 / 𝑆)

Proof of Theorem dmqseqi

Step	Hyp	Ref	Expression
1		dmqseqi.1	. 2 ⊢ 𝑅 = 𝑆
2		dmqseq 39859	. 2 ⊢ (𝑅 = 𝑆 → (dom 𝑅 / 𝑅) = (dom 𝑆 / 𝑆))
3	1, 2	ax-mp 5	1 ⊢ (dom 𝑅 / 𝑅) = (dom 𝑆 / 𝑆)

This proof depends on syntax axioms:   = wceq 1570  dom cdm 5656   / cqs 8747

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-rex 3091  df-rab 3417  df-v 3456  df-ss 3901  df-dif 4050  df-in 4094  df-un 4154  df-nul 4282  df-if 4486  df-sn 4589  df-pr 4591  df-op 4839  df-br 5107  df-opab 5172  df-cnv 5664  df-dm 5666  df-rn 5667  df-res 5668  df-ima 5669  df-ec 8750  df-qs 8754

This theorem is used by: (None)