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Metamath Proof Explorer

Theorem spimev

Description: Distinct-variable version of spime . (Contributed by NM, 10-Jan-1993) Usage of this theorem is discouraged because it depends on ax-13 . Use spimevw instead. (New usage is discouraged.)

		Ref	Expression
	Hypothesis	spimev.1	⊢ ( 𝑥 = 𝑦 → ( 𝜑 → 𝜓 ) )
	Assertion	spimev	⊢ ( 𝜑 → ∃ 𝑥 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		spimev.1	⊢ ( 𝑥 = 𝑦 → ( 𝜑 → 𝜓 ) )
2		nfv	⊢ Ⅎ 𝑥 𝜑
3	2 1	spime	⊢ ( 𝜑 → ∃ 𝑥 𝜓 )