Theorem el3v2

Description: New way ( elv , and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 16-Oct-2020)

	Ref	Expression
Hypothesis	el3v2.1	⊢ ( ( 𝜑 ∧ 𝑦 ∈ V ∧ 𝜒 ) → 𝜃 )
Assertion	el3v2	⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		el3v2.1	⊢ ( ( 𝜑 ∧ 𝑦 ∈ V ∧ 𝜒 ) → 𝜃 )
2		vex	⊢ 𝑦 ∈ V
3	2 1	mp3an2	⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 )