Metamath Proof Explorer


Theorem pwuninel2

Description: Direct proof of pwuninel avoiding functions and thus several ZF axioms. (Contributed by Stefan O'Rear, 22-Feb-2015)

Ref Expression
Assertion pwuninel2 ( 𝐴𝑉 → ¬ 𝒫 𝐴𝐴 )

Proof

Step Hyp Ref Expression
1 pwnss ( 𝐴𝑉 → ¬ 𝒫 𝐴 𝐴 )
2 elssuni ( 𝒫 𝐴𝐴 → 𝒫 𝐴 𝐴 )
3 1 2 nsyl ( 𝐴𝑉 → ¬ 𝒫 𝐴𝐴 )