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	$$⊢\psi \leftrightarrow \chi$$
Assertion	mobii	$$⊢{\exists }^{*}x\psi \leftrightarrow {\exists }^{*}x\chi$$

Proof

Step	Hyp	Ref	Expression
1		mobii.1	$$⊢\psi \leftrightarrow \chi$$
2		mobi	$$⊢\forall x\left(\psi \leftrightarrow \chi \right)\to \left({\exists }^{*}x\psi \leftrightarrow {\exists }^{*}x\chi \right)$$
3	2 1	mpg	$$⊢{\exists }^{*}x\psi \leftrightarrow {\exists }^{*}x\chi$$