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Metamath Proof Explorer

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	⊢ ( ( 𝜑 ∧ 𝑥 ∈ V ) → 𝜓 )
	Assertion	elvd	⊢ ( 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		elvd.1	⊢ ( ( 𝜑 ∧ 𝑥 ∈ V ) → 𝜓 )
2		vex	⊢ 𝑥 ∈ V
3	2 1	mpan2	⊢ ( 𝜑 → 𝜓 )