Theorem el3v3

Description: If a proposition is implied by z e. _V (which is true, see vex ) and two other antecedents, then it is implied by these other antecedents. (Contributed by Peter Mazsa, 16-Oct-2020)

	Ref	Expression
Hypothesis	el3v3.1	$$⊢\left(\phi \wedge \psi \wedge z\in \mathrm{V}\right)\to \theta$$
Assertion	el3v3	$$⊢\left(\phi \wedge \psi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		el3v3.1	$$⊢\left(\phi \wedge \psi \wedge z\in \mathrm{V}\right)\to \theta$$
2		vex	$$⊢z\in \mathrm{V}$$
3	2 1	mp3an3	$$⊢\left(\phi \wedge \psi \right)\to \theta$$