Theorem el2v

Description: If a proposition is implied by x e.V and y e. V (which is true, see vex ), then it is true. (Contributed by Peter Mazsa, 13-Oct-2018)

	Ref	Expression
Hypothesis	el2v.1	⊢ ( ( 𝑥 ∈ V ∧ 𝑦 ∈ V ) → 𝜑 )
Assertion	el2v	⊢ 𝜑

Proof

Step	Hyp	Ref	Expression
1		el2v.1	⊢ ( ( 𝑥 ∈ V ∧ 𝑦 ∈ V ) → 𝜑 )
2		vex	⊢ 𝑥 ∈ V
3		vex	⊢ 𝑦 ∈ V
4	2 3 1	mp2an	⊢ 𝜑