Theorem ssrexvOLD

Description: Obsolete version of ssrexv as of 19-May-2025. (Contributed by NM, 11-Jan-2007) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	ssrexvOLD	⊢ ( 𝐴 ⊆ 𝐵 → ( ∃ 𝑥 ∈ 𝐴 𝜑 → ∃ 𝑥 ∈ 𝐵 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		ssel	⊢ ( 𝐴 ⊆ 𝐵 → ( 𝑥 ∈ 𝐴 → 𝑥 ∈ 𝐵 ) )
2	1	anim1d	⊢ ( 𝐴 ⊆ 𝐵 → ( ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) → ( 𝑥 ∈ 𝐵 ∧ 𝜑 ) ) )
3	2	reximdv2	⊢ ( 𝐴 ⊆ 𝐵 → ( ∃ 𝑥 ∈ 𝐴 𝜑 → ∃ 𝑥 ∈ 𝐵 𝜑 ) )