Metamath Proof Explorer


Theorem el3v13

Description: New way ( elv , and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 11-Jul-2021)

Ref Expression
Hypothesis el3v13.1 ⊢ x ∈ V ∧ ψ ∧ z ∈ V → θ
Assertion el3v13 ⊢ ψ → θ

Proof

Step Hyp Ref Expression
1 el3v13.1 ⊢ x ∈ V ∧ ψ ∧ z ∈ V → θ
2 1 el3v3 ⊢ x ∈ V ∧ ψ → θ
3 2 el2v1 ⊢ ψ → θ