Theorem parteq1i

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

	Ref	Expression
Hypothesis	parteq1i.1	⊢ 𝑅 = 𝑆
Assertion	parteq1i	⊢ ( 𝑅 Part 𝐴 ↔ 𝑆 Part 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		parteq1i.1	⊢ 𝑅 = 𝑆
2		parteq1	⊢ ( 𝑅 = 𝑆 → ( 𝑅 Part 𝐴 ↔ 𝑆 Part 𝐴 ) )
3	1 2	ax-mp	⊢ ( 𝑅 Part 𝐴 ↔ 𝑆 Part 𝐴 )