Theorem nd4

Description: A lemma for proving conditionless ZFC axioms. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 2-Jan-2002) (New usage is discouraged.)

	Ref	Expression
Assertion	nd4	⊢ ( ∀ 𝑥 𝑥 = 𝑦 → ¬ ∀ 𝑧 𝑦 ∈ 𝑥 )

Proof

Step	Hyp	Ref	Expression
1		nd3	⊢ ( ∀ 𝑦 𝑦 = 𝑥 → ¬ ∀ 𝑧 𝑦 ∈ 𝑥 )
2	1	aecoms	⊢ ( ∀ 𝑥 𝑥 = 𝑦 → ¬ ∀ 𝑧 𝑦 ∈ 𝑥 )