Theorem inex3 38320

Description: Sufficient condition for the intersection relation to be a set. (Contributed by Peter Mazsa, 24-Nov-2019.)

Assertion

Ref	Expression
inex3	⊢ ((𝐴 ∈ 𝑉 ∨ 𝐵 ∈ 𝑊) → (𝐴 ∩ 𝐵) ∈ V)

Proof of Theorem inex3

Step	Hyp	Ref	Expression
1		inex1g 5325	. 2 ⊢ (𝐴 ∈ 𝑉 → (𝐴 ∩ 𝐵) ∈ V)
2		inex2g 5326	. 2 ⊢ (𝐵 ∈ 𝑊 → (𝐴 ∩ 𝐵) ∈ V)
3	1, 2	jaoi 857	1 ⊢ ((𝐴 ∈ 𝑉 ∨ 𝐵 ∈ 𝑊) → (𝐴 ∩ 𝐵) ∈ V)

Syntax hints:   → wi 4   ∨ wo 847   ∈ wcel 2106  Vcvv 3478   ∩ cin 3962

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706  ax-sep 5302

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-rab 3434  df-v 3480  df-in 3970

This theorem is referenced by: (None)