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Metamath Proof Explorer

Theorem 19.40

Description: Theorem 19.40 of Margaris p. 90. (Contributed by NM, 26-May-1993)

		Ref	Expression
	Assertion	19.40	⊢ ( ∃ 𝑥 ( 𝜑 ∧ 𝜓 ) → ( ∃ 𝑥 𝜑 ∧ ∃ 𝑥 𝜓 ) )

Step	Hyp	Ref	Expression
1		exsimpl	⊢ ( ∃ 𝑥 ( 𝜑 ∧ 𝜓 ) → ∃ 𝑥 𝜑 )
2		exsimpr	⊢ ( ∃ 𝑥 ( 𝜑 ∧ 𝜓 ) → ∃ 𝑥 𝜓 )
3	1 2	jca	⊢ ( ∃ 𝑥 ( 𝜑 ∧ 𝜓 ) → ( ∃ 𝑥 𝜑 ∧ ∃ 𝑥 𝜓 ) )