Theorem r1sssucd

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

	Ref	Expression
Hypothesis	r1sssucd.1	⊢ ( 𝜑 → 𝐴 ∈ On )
Assertion	r1sssucd	⊢ ( 𝜑 → ( 𝑅1 ‘ 𝐴 ) ⊆ ( 𝑅1 ‘ suc 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		r1sssucd.1	⊢ ( 𝜑 → 𝐴 ∈ On )
2		r1sssuc	⊢ ( 𝐴 ∈ On → ( 𝑅1 ‘ 𝐴 ) ⊆ ( 𝑅1 ‘ suc 𝐴 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝑅1 ‘ 𝐴 ) ⊆ ( 𝑅1 ‘ suc 𝐴 ) )