Theorem mobii

Description: Formula-building rule for the at-most-one quantifier (inference form). (Contributed by NM, 9-Mar-1995) (Revised by Mario Carneiro, 17-Oct-2016)

	Ref	Expression
Hypothesis	mobii.1	⊢ ( 𝜓 ↔ 𝜒 )
Assertion	mobii	⊢ ( ∃* 𝑥 𝜓 ↔ ∃* 𝑥 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		mobii.1	⊢ ( 𝜓 ↔ 𝜒 )
2		mobi	⊢ ( ∀ 𝑥 ( 𝜓 ↔ 𝜒 ) → ( ∃* 𝑥 𝜓 ↔ ∃* 𝑥 𝜒 ) )
3	2 1	mpg	⊢ ( ∃* 𝑥 𝜓 ↔ ∃* 𝑥 𝜒 )