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Metamath Proof Explorer

Theorem qseq2i

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

Ref Expression
Hypothesis qseq2i.1 ⊢ 𝐴 = 𝐵
Assertion qseq2i ( 𝐶 / 𝐴 ) = ( 𝐶 / 𝐵 )

Proof

Step Hyp Ref Expression
1 qseq2i.1 ⊢ 𝐴 = 𝐵
2 qseq2 ⊢ ( 𝐴 = 𝐵 → ( 𝐶 / 𝐴 ) = ( 𝐶 / 𝐵 ) )
3 1 2 ax-mp ⊢ ( 𝐶 / 𝐴 ) = ( 𝐶 / 𝐵 )