exa1 - Metamath Proof Explorer

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Theorem exa1 1833

Description: Add an antecedent in an existentially quantified formula. (Contributed by BJ, 6-Oct-2018.)

**Assertion**
Ref	Expression
exa1	⊢ (∃𝑥𝜑 → ∃𝑥(𝜓 → 𝜑))

**Proof of Theorem exa1**
Step	Hyp	Ref	Expression
1		ax-1 6	. 2 ⊢ (𝜑 → (𝜓 → 𝜑))
2	1	eximi 1830	1 ⊢ (∃𝑥𝜑 → ∃𝑥(𝜓 → 𝜑))

Colors of variables: wff setvar class

Syntax hints: → wi 4 ∃wex 1774

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804

This theorem depends on definitions: df-bi 206 df-ex 1775

This theorem is referenced by: 19.35 1873

	
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