Theorem inv2 35476

Description: The intersection of the universal class with a class is itself. A commuted form of inv1 4354. (Contributed by BTernaryTau, 24-Jun-2026.)

Assertion

Ref	Expression
inv2	⊢ (V ∩ 𝐴) = 𝐴

Proof of Theorem inv2

Step	Hyp	Ref	Expression
1		inv1 4354	. 2 ⊢ (𝐴 ∩ V) = 𝐴
2	1	ineqcomi 4163	1 ⊢ (V ∩ 𝐴) = 𝐴

This proof depends on syntax axioms:   = wceq 1569  Vcvv 3454   ∩ cin 3903

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-8 2144  ax-9 2152  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 401  df-tru 1572  df-ex 1809  df-sb 2096  df-clab 2741  df-cleq 2754  df-clel 2837  df-rab 3416  df-v 3456  df-in 3911  df-ss 3921

This theorem is used by:  dfscott3  35521