Theorem inv2 35643

Description: The intersection of the universal class with a class is itself. A commuted form of inv1 4347. (Contributed by BTernaryTau, 24-Jun-2026.)

Assertion

Ref	Expression
inv2	⊢ (V ∩ 𝐴) = 𝐴

Proof of Theorem inv2

Step	Hyp	Ref	Expression
1		inv1 4347	. 2 ⊢ (𝐴 ∩ V) = 𝐴
2	1	ineqcomi 4156	1 ⊢ (V ∩ 𝐴) = 𝐴

This proof depends on syntax axioms:   = wceq 1570  Vcvv 3450   ∩ cin 3897

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 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-rab 3413  df-v 3452  df-in 3905  df-ss 3915

This theorem is used by:  dfscott3  35673