Theorem dmqseqi 39060

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 39059	. 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 1542  dom cdm 5624   / cqs 8635

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 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-rex 3063  df-rab 3391  df-v 3432  df-dif 3893  df-un 3895  df-in 3897  df-ss 3907  df-nul 4275  df-if 4468  df-sn 4569  df-pr 4571  df-op 4575  df-br 5087  df-opab 5149  df-cnv 5632  df-dm 5634  df-rn 5635  df-res 5636  df-ima 5637  df-ec 8638  df-qs 8642

This theorem is referenced by: (None)