Theorem reximiaOLD

Description: Obsolete version of reximia as of 31-Oct-2024. (Contributed by NM, 10-Feb-1997) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	reximiaOLD.1	⊢ ( 𝑥 ∈ 𝐴 → ( 𝜑 → 𝜓 ) )
Assertion	reximiaOLD	⊢ ( ∃ 𝑥 ∈ 𝐴 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		reximiaOLD.1	⊢ ( 𝑥 ∈ 𝐴 → ( 𝜑 → 𝜓 ) )
2		rexim	⊢ ( ∀ 𝑥 ∈ 𝐴 ( 𝜑 → 𝜓 ) → ( ∃ 𝑥 ∈ 𝐴 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜓 ) )
3	2 1	mprg	⊢ ( ∃ 𝑥 ∈ 𝐴 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜓 )