Theorem dmqseqi 38626

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 38625	. 2 ⊢ (𝑅 = 𝑆 → (dom 𝑅 / 𝑅) = (dom 𝑆 / 𝑆))
3	1, 2	ax-mp 5	1 ⊢ (dom 𝑅 / 𝑅) = (dom 𝑆 / 𝑆)

Syntax hints:   = wceq 1540  dom cdm 5646   / cqs 8681

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-rex 3056  df-rab 3412  df-v 3457  df-dif 3925  df-un 3927  df-in 3929  df-ss 3939  df-nul 4305  df-if 4497  df-sn 4598  df-pr 4600  df-op 4604  df-br 5116  df-opab 5178  df-cnv 5654  df-dm 5656  df-rn 5657  df-res 5658  df-ima 5659  df-ec 8684  df-qs 8688

This theorem is referenced by: (None)