Metamath Proof Explorer


Theorem el3v23

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 el3v23.1 ( ( 𝜑𝑦 ∈ V ∧ 𝑧 ∈ V ) → 𝜃 )
Assertion el3v23 ( 𝜑𝜃 )

Proof

Step Hyp Ref Expression
1 el3v23.1 ( ( 𝜑𝑦 ∈ V ∧ 𝑧 ∈ V ) → 𝜃 )
2 1 el3v3 ( ( 𝜑𝑦 ∈ V ) → 𝜃 )
3 2 elvd ( 𝜑𝜃 )