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Metamath Proof Explorer

Theorem dmqseqd

Description: Equality theorem for domain quotient set, deduction version. (Contributed by Peter Mazsa, 23-Apr-2021)

Ref Expression
Hypothesis dmqseqd.1 ⊢ ( 𝜑 → 𝑅 = 𝑆 )
Assertion dmqseqd ( 𝜑 → ( dom 𝑅 / 𝑅 ) = ( dom 𝑆 / 𝑆 ) )

Proof

Step Hyp Ref Expression
1 dmqseqd.1 ⊢ ( 𝜑 → 𝑅 = 𝑆 )
2 dmqseq ⊢ ( 𝑅 = 𝑆 → ( dom 𝑅 / 𝑅 ) = ( dom 𝑆 / 𝑆 ) )
3 1 2 syl ⊢ ( 𝜑 → ( dom 𝑅 / 𝑅 ) = ( dom 𝑆 / 𝑆 ) )