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Metamath Proof Explorer

Theorem exlimiiv

Description: Inference (Rule C) associated with exlimiv . (Contributed by BJ, 19-Dec-2020)

Ref Expression
Hypotheses exlimiv.1 ⊢ ( 𝜑 → 𝜓 )
exlimiiv.2 ⊢ ∃ 𝑥 𝜑
Assertion exlimiiv 𝜓

Proof

Step Hyp Ref Expression
1 exlimiv.1 ⊢ ( 𝜑 → 𝜓 )
2 exlimiiv.2 ⊢ ∃ 𝑥 𝜑
3 1 exlimiv ⊢ ( ∃ 𝑥 𝜑 → 𝜓 )
4 2 3 ax-mp ⊢ 𝜓