Theorem el3v

Description: New way ( elv , and the theorems beginning with "el2v" or "el3v") to shorten some proofs. Inference forms (with |- A e.V , |- B e. V and |- C e. _V hypotheses) of the general theorems (proving |- ( ( A e. V /\ B e. W /\ C e. X ) -> assertions) may be superfluous. (Contributed by Peter Mazsa, 13-Oct-2018)

	Ref	Expression
Hypothesis	el3v.1	⊢ ( ( 𝑥 ∈ V ∧ 𝑦 ∈ V ∧ 𝑧 ∈ V ) → 𝜑 )
Assertion	el3v	⊢ 𝜑

Proof

Step	Hyp	Ref	Expression
1		el3v.1	⊢ ( ( 𝑥 ∈ V ∧ 𝑦 ∈ V ∧ 𝑧 ∈ V ) → 𝜑 )
2		vex	⊢ 𝑥 ∈ V
3		vex	⊢ 𝑦 ∈ V
4		vex	⊢ 𝑧 ∈ V
5	2 3 4 1	mp3an	⊢ 𝜑