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Metamath Proof Explorer

Theorem equsb1

Description: Substitution applied to an atomic wff. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker equsb1v if possible. (Contributed by NM, 10-May-1993) (New usage is discouraged.)

		Ref	Expression
	Assertion	equsb1	⊢ [ 𝑦 / 𝑥 ] 𝑥 = 𝑦

Proof

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