This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem sbequ5

Description: Substitution does not change an identical variable specifier. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 15-May-1993) (New usage is discouraged.)

		Ref	Expression
	Assertion	sbequ5	⊢ ( [ 𝑤 / 𝑧 ] ∀ 𝑥 𝑥 = 𝑦 ↔ ∀ 𝑥 𝑥 = 𝑦 )

Proof

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