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

Metamath Proof Explorer

Theorem parteq1d

Description: Equality theorem for partition, deduction version. (Contributed by Peter Mazsa, 5-Oct-2021)

Ref Expression
Hypothesis parteq1d.1 ⊢ ( 𝜑 → 𝑅 = 𝑆 )
Assertion parteq1d ( 𝜑 → ( 𝑅 Part 𝐴 ↔ 𝑆 Part 𝐴 ) )

Proof

Step Hyp Ref Expression
1 parteq1d.1 ⊢ ( 𝜑 → 𝑅 = 𝑆 )
2 parteq1 ⊢ ( 𝑅 = 𝑆 → ( 𝑅 Part 𝐴 ↔ 𝑆 Part 𝐴 ) )
3 1 2 syl ⊢ ( 𝜑 → ( 𝑅 Part 𝐴 ↔ 𝑆 Part 𝐴 ) )