Theorem elvd

Description: If a proposition is implied by x e. _V (which is true, see vex ) and another antecedent, then it is implied by that other antecedent. Deduction associated with elv . (Contributed by Peter Mazsa, 23-Oct-2018)

	Ref	Expression
Hypothesis	elvd.1	$$⊢\left(\phi \wedge x\in \mathrm{V}\right)\to \psi$$
Assertion	elvd	$$⊢\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		elvd.1	$$⊢\left(\phi \wedge x\in \mathrm{V}\right)\to \psi$$
2		vex	$$⊢x\in \mathrm{V}$$
3	2 1	mpan2	$$⊢\phi \to \psi$$