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Metamath Proof Explorer

Theorem qseq1i

Description: Equality theorem for quotient set, inference form. (Contributed by Peter Mazsa, 3-Jun-2021)

Ref Expression
Hypothesis qseq1i.1 ⊢ A = B
Assertion qseq1i ⊢ A / C = B / C

Proof

Step Hyp Ref Expression
1 qseq1i.1 ⊢ A = B
2 qseq1 ⊢ A = B → A / C = B / C
3 1 2 ax-mp ⊢ A / C = B / C