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Metamath Proof Explorer

Theorem iotasbc5

Description: Theorem *14.205 in WhiteheadRussell p. 190. (Contributed by Andrew Salmon, 11-Jul-2011)

		Ref	Expression
	Assertion	iotasbc5	$⊢ \exists! x φ \to (\underset{˙}{[} (ι x \| φ) / y \underset{˙}{]} ψ \leftrightarrow \exists y (y = (ι x \| φ) \land ψ))$

Step	Hyp	Ref	Expression
1		sbc5	$⊢ \underset{˙}{[} (ι x \| φ) / y \underset{˙}{]} ψ \leftrightarrow \exists y (y = (ι x \| φ) \land ψ)$
2	1	a1i	$⊢ \exists! x φ \to (\underset{˙}{[} (ι x \| φ) / y \underset{˙}{]} ψ \leftrightarrow \exists y (y = (ι x \| φ) \land ψ))$