Theorem bnj132

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Proof shortened by Andrew Salmon, 26-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypothesis	bnj132.1	$$⊢\phi \leftrightarrow \exists x\left(\psi \to \chi \right)$$
Assertion	bnj132	$$⊢\phi \leftrightarrow \left(\psi \to \exists x\chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bnj132.1	$$⊢\phi \leftrightarrow \exists x\left(\psi \to \chi \right)$$
2		19.37v	$$⊢\exists x\left(\psi \to \chi \right)\leftrightarrow \left(\psi \to \exists x\chi \right)$$
3	1 2	bitri	$$⊢\phi \leftrightarrow \left(\psi \to \exists x\chi \right)$$