Theorem pm10.12

Description: Theorem *10.12 in WhiteheadRussell p. 146. In *10, this is treated as an axiom, and the proofs in *10 are based on this theorem. (Contributed by Andrew Salmon, 17-Jun-2011)

	Ref	Expression
Assertion	pm10.12	$$⊢\forall x\left(\phi \vee \psi \right)\to \left(\phi \vee \forall x\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		19.32v	$$⊢\forall x\left(\phi \vee \psi \right)\leftrightarrow \left(\phi \vee \forall x\psi \right)$$
2	1	biimpi	$$⊢\forall x\left(\phi \vee \psi \right)\to \left(\phi \vee \forall x\psi \right)$$