Metamath Proof Explorer


Theorem bj-nnfed

Description: Nonfreeness implies the equivalent of ax5e , deduction form. (Contributed by BJ, 2-Dec-2023)

Ref Expression
Hypothesis bj-nnfed.1 ( 𝜑 → Ⅎ' 𝑥 𝜓 )
Assertion bj-nnfed ( 𝜑 → ( ∃ 𝑥 𝜓𝜓 ) )

Proof

Step Hyp Ref Expression
1 bj-nnfed.1 ( 𝜑 → Ⅎ' 𝑥 𝜓 )
2 bj-nnfe ( Ⅎ' 𝑥 𝜓 → ( ∃ 𝑥 𝜓𝜓 ) )
3 1 2 syl ( 𝜑 → ( ∃ 𝑥 𝜓𝜓 ) )