Theorem exsimpr

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	exsimpr	⊢ ( ∃ 𝑥 ( 𝜑 ∧ 𝜓 ) → ∃ 𝑥 𝜓 )

Proof

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