Theorem inv2 35781

Description: The intersection of the universal class with a class is itself. A commuted form of inv1 4351. (Contributed by BTernaryTau, 24-Jun-2026.)

Assertion

Ref	Expression
inv2	⊢ (V ∩ 𝐴) = 𝐴

Proof of Theorem inv2

Step	Hyp	Ref	Expression
1		inv1 4351	. 2 ⊢ (𝐴 ∩ V) = 𝐴
2	1	ineqcomi 4111	1 ⊢ (V ∩ 𝐴) = 𝐴

This proof depends on syntax axioms:   = wceq 1570  Vcvv 3454   ∩ cin 4092

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-rab 3417  df-v 3456  df-ss 3901  df-in 4094

This theorem is used by:  dfscott3  35827