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Metamath Proof Explorer

Theorem sbequ6

Description: Substitution does not change a distinctor. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 5-Aug-1993) (New usage is discouraged.)

		Ref	Expression
	Assertion	sbequ6	⊢ ( [ 𝑤 / 𝑧 ] ¬ ∀ 𝑥 𝑥 = 𝑦 ↔ ¬ ∀ 𝑥 𝑥 = 𝑦 )

Proof

Step	Hyp	Ref	Expression
1		nfnae	⊢ Ⅎ 𝑧 ¬ ∀ 𝑥 𝑥 = 𝑦
2	1	sbf	⊢ ( [ 𝑤 / 𝑧 ] ¬ ∀ 𝑥 𝑥 = 𝑦 ↔ ¬ ∀ 𝑥 𝑥 = 𝑦 )