Theorem reximddv3

Description: Deduction from Theorem 19.22 of Margaris p. 90. (Contributed by Glauco Siliprandi, 5-Feb-2022)

	Ref	Expression
Hypotheses	reximddv3.1	⊢ ( ( ( 𝜑 ∧ 𝑥 ∈ 𝐴 ) ∧ 𝜓 ) → 𝜒 )
	reximddv3.2	⊢ ( 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜓 )
Assertion	reximddv3	⊢ ( 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		reximddv3.1	⊢ ( ( ( 𝜑 ∧ 𝑥 ∈ 𝐴 ) ∧ 𝜓 ) → 𝜒 )
2		reximddv3.2	⊢ ( 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜓 )
3	1	anasss	⊢ ( ( 𝜑 ∧ ( 𝑥 ∈ 𝐴 ∧ 𝜓 ) ) → 𝜒 )
4	3 2	reximddv	⊢ ( 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜒 )