Theorem r1sssucd

Description: Deductive form of r1sssuc . (Contributed by Noam Pasman, 19-Jan-2025)

	Ref	Expression
Hypothesis	r1sssucd.1	$$⊢\phi \to A\in \mathrm{On}$$
Assertion	r1sssucd	$$⊢\phi \to R_1\left(A\right)\subseteq R_1\left(\mathrm{suc}A\right)$$

Proof

Step	Hyp	Ref	Expression
1		r1sssucd.1	$$⊢\phi \to A\in \mathrm{On}$$
2		r1sssuc	$$⊢A\in \mathrm{On}\to R_1\left(A\right)\subseteq R_1\left(\mathrm{suc}A\right)$$
3	1 2	syl	$$⊢\phi \to R_1\left(A\right)\subseteq R_1\left(\mathrm{suc}A\right)$$