Theorem inv2 35433

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

Syntax hints:   = wceq 1568  Vcvv 3453   ∩ cin 3903

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-8 2143  ax-9 2151  ax-ext 2733

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1571  df-ex 1808  df-sb 2095  df-clab 2740  df-cleq 2753  df-clel 2836  df-rab 3415  df-v 3455  df-in 3911  df-ss 3921

This theorem is referenced by:  dfscott3  35478