Theorem 19.17

Description: Theorem 19.17 of Margaris p. 90. (Contributed by NM, 12-Mar-1993)

	Ref	Expression
Hypothesis	19.17.1	$$⊢Ⅎx\psi$$
Assertion	19.17	$$⊢\forall x\left(\phi \leftrightarrow \psi \right)\to \left(\forall x\phi \leftrightarrow \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		19.17.1	$$⊢Ⅎx\psi$$
2		albi	$$⊢\forall x\left(\phi \leftrightarrow \psi \right)\to \left(\forall x\phi \leftrightarrow \forall x\psi \right)$$
3	1	19.3	$$⊢\forall x\psi \leftrightarrow \psi$$
4	2 3	bitrdi	$$⊢\forall x\left(\phi \leftrightarrow \psi \right)\to \left(\forall x\phi \leftrightarrow \psi \right)$$