This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

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