Metamath Proof Explorer


Theorem qseq12d

Description: Equality theorem for quotient set, deduction form. (Contributed by Steven Nguyen, 30-Apr-2023)

Ref Expression
Hypotheses qseq12d.1 φ A = B
qseq12d.2 φ C = D
Assertion qseq12d φ A / C = B / D

Proof

Step Hyp Ref Expression
1 qseq12d.1 φ A = B
2 qseq12d.2 φ C = D
3 qseq12 A = B C = D A / C = B / D
4 1 2 3 syl2anc φ A / C = B / D