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

Metamath Proof Explorer

Theorem equsb2

Description: Substitution applied to an atomic wff. Usage of this theorem is discouraged because it depends on ax-13 . Check out equsb1v for a version requiring fewer axioms. (Contributed by NM, 10-May-1993) (New usage is discouraged.)

		Ref	Expression
	Assertion	equsb2	⊢ [ 𝑦 / 𝑥 ] 𝑦 = 𝑥

Proof

Step	Hyp	Ref	Expression
1		sb2	⊢ ( ∀ 𝑥 ( 𝑥 = 𝑦 → 𝑦 = 𝑥 ) → [ 𝑦 / 𝑥 ] 𝑦 = 𝑥 )
2		equcomi	⊢ ( 𝑥 = 𝑦 → 𝑦 = 𝑥 )
3	1 2	mpg	⊢ [ 𝑦 / 𝑥 ] 𝑦 = 𝑥