Theorem pm14.18

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

	Ref	Expression
Assertion	pm14.18	$$⊢\exists !x\phi \to \left(\forall x\psi \to \underset{\dot{}}{[}\left(\iota x|\phi \right)/x\underset{\dot{}}{]}\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		iotaexeu	$$⊢\exists !x\phi \to \left(\iota x|\phi \right)\in \mathrm{V}$$
2		spsbc	$$⊢\left(\iota x|\phi \right)\in \mathrm{V}\to \left(\forall x\psi \to \underset{\dot{}}{[}\left(\iota x|\phi \right)/x\underset{\dot{}}{]}\psi \right)$$
3	1 2	syl	$$⊢\exists !x\phi \to \left(\forall x\psi \to \underset{\dot{}}{[}\left(\iota x|\phi \right)/x\underset{\dot{}}{]}\psi \right)$$