Theorem pm10.42

Description: Theorem *10.42 in WhiteheadRussell p. 155. (Contributed by Andrew Salmon, 17-Jun-2011)

	Ref	Expression
Assertion	pm10.42	$$⊢\left(\exists x\phi \vee \exists x\psi \right)\leftrightarrow \exists x\left(\phi \vee \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		19.43	$$⊢\exists x\left(\phi \vee \psi \right)\leftrightarrow \left(\exists x\phi \vee \exists x\psi \right)$$
2	1	bicomi	$$⊢\left(\exists x\phi \vee \exists x\psi \right)\leftrightarrow \exists x\left(\phi \vee \psi \right)$$