Theorem parteq1d

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

	Ref	Expression
Hypothesis	parteq1d.1	$$⊢\phi \to R=S$$
Assertion	parteq1d	$$⊢\phi \to \left(RPartA\leftrightarrow SPartA\right)$$

Proof

Step	Hyp	Ref	Expression
1		parteq1d.1	$$⊢\phi \to R=S$$
2		parteq1	$$⊢R=S\to \left(RPartA\leftrightarrow SPartA\right)$$
3	1 2	syl	$$⊢\phi \to \left(RPartA\leftrightarrow SPartA\right)$$