Metamath Proof Explorer


Theorem dmqseqeq1d

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

Ref Expression
Hypothesis dmqseqeq1d.1 φ R = S
Assertion dmqseqeq1d φ dom R / R = A dom S / S = A

Proof

Step Hyp Ref Expression
1 dmqseqeq1d.1 φ R = S
2 dmqseqeq1 R = S dom R / R = A dom S / S = A
3 1 2 syl φ dom R / R = A dom S / S = A