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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 → [ ( ℩ 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 ) )