Metamath Proof Explorer


Theorem el3v12

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 el3v12.1 ⊢ x ∈ V ∧ y ∈ V ∧ χ → θ
Assertion el3v12 ⊢ χ → θ

Proof

Step Hyp Ref Expression
1 el3v12.1 ⊢ x ∈ V ∧ y ∈ V ∧ χ → θ
2 1 el3v1 ⊢ y ∈ V ∧ χ → θ
3 2 el2v1 ⊢ χ → θ