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Metamath Proof Explorer

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 )