Theorem iotasbcq

Description: Theorem *14.272 in WhiteheadRussell p. 193. (Contributed by Andrew Salmon, 11-Jul-2011)

	Ref	Expression
Assertion	iotasbcq	⊢ ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) → ( [ ( ℩ 𝑥 𝜑 ) / 𝑦 ] 𝜒 ↔ [ ( ℩ 𝑥 𝜓 ) / 𝑦 ] 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		iotabi	⊢ ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) → ( ℩ 𝑥 𝜑 ) = ( ℩ 𝑥 𝜓 ) )
2	1	sbceq1d	⊢ ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) → ( [ ( ℩ 𝑥 𝜑 ) / 𝑦 ] 𝜒 ↔ [ ( ℩ 𝑥 𝜓 ) / 𝑦 ] 𝜒 ) )