Theorem albitr

Description: Theorem *10.301 in WhiteheadRussell p. 151. (Contributed by Andrew Salmon, 24-May-2011)

	Ref	Expression
Assertion	albitr	$$⊢\left(\forall x\left(\phi \leftrightarrow \psi \right)\wedge \forall x\left(\psi \leftrightarrow \chi \right)\right)\to \forall x\left(\phi \leftrightarrow \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bitr	$$⊢\left(\left(\phi \leftrightarrow \psi \right)\wedge \left(\psi \leftrightarrow \chi \right)\right)\to \left(\phi \leftrightarrow \chi \right)$$
2	1	alanimi	$$⊢\left(\forall x\left(\phi \leftrightarrow \psi \right)\wedge \forall x\left(\psi \leftrightarrow \chi \right)\right)\to \forall x\left(\phi \leftrightarrow \chi \right)$$