Description: Equality theorem for domain quotient. (Contributed by Peter Mazsa, 17-Apr-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | dmqseqeq1 | ⊢ ( 𝑅 = 𝑆 → ( ( dom 𝑅 / 𝑅 ) = 𝐴 ↔ ( dom 𝑆 / 𝑆 ) = 𝐴 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmqseq | ⊢ ( 𝑅 = 𝑆 → ( dom 𝑅 / 𝑅 ) = ( dom 𝑆 / 𝑆 ) ) | |
2 | 1 | eqeq1d | ⊢ ( 𝑅 = 𝑆 → ( ( dom 𝑅 / 𝑅 ) = 𝐴 ↔ ( dom 𝑆 / 𝑆 ) = 𝐴 ) ) |