Theorem pm14.18

Description: Theorem *14.18 in WhiteheadRussell p. 189. (Contributed by Andrew Salmon, 11-Jul-2011)

	Ref	Expression
Assertion	pm14.18	⊢ ( ∃! 𝑥 𝜑 → ( ∀ 𝑥 𝜓 → [ ( ℩ 𝑥 𝜑 ) / 𝑥 ] 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		iotaexeu	⊢ ( ∃! 𝑥 𝜑 → ( ℩ 𝑥 𝜑 ) ∈ V )
2		spsbc	⊢ ( ( ℩ 𝑥 𝜑 ) ∈ V → ( ∀ 𝑥 𝜓 → [ ( ℩ 𝑥 𝜑 ) / 𝑥 ] 𝜓 ) )
3	1 2	syl	⊢ ( ∃! 𝑥 𝜑 → ( ∀ 𝑥 𝜓 → [ ( ℩ 𝑥 𝜑 ) / 𝑥 ] 𝜓 ) )