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Metamath Proof Explorer

Theorem exsimpl

Description: Simplification of an existentially quantified conjunction. (Contributed by Rodolfo Medina, 25-Sep-2010) (Proof shortened by Andrew Salmon, 29-Jun-2011)

		Ref	Expression
	Assertion	exsimpl	⊢ ( ∃ 𝑥 ( 𝜑 ∧ 𝜓 ) → ∃ 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		simpl	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜑 )
2	1	eximi	⊢ ( ∃ 𝑥 ( 𝜑 ∧ 𝜓 ) → ∃ 𝑥 𝜑 )