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Metamath Proof Explorer

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 → [˙ ι x | φ / x]˙ ψ

Proof

Step Hyp Ref Expression
1 iotaexeu ⊢ ∃! x φ → ι x | φ ∈ V
2 spsbc ⊢ ι x | φ ∈ V → ∀ x ψ → [˙ ι x | φ / x]˙ ψ
3 1 2 syl ⊢ ∃! x φ → ∀ x ψ → [˙ ι x | φ / x]˙ ψ