Theorem eqsb1

Description: Substitution for the left-hand side in an equality. Class version of equsb3 . (Contributed by Rodolfo Medina, 28-Apr-2010)

	Ref	Expression
Assertion	eqsb1	⊢ ( [ 𝑦 / 𝑥 ] 𝑥 = 𝐴 ↔ 𝑦 = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		eqeq1	⊢ ( 𝑥 = 𝑤 → ( 𝑥 = 𝐴 ↔ 𝑤 = 𝐴 ) )
2		eqeq1	⊢ ( 𝑤 = 𝑦 → ( 𝑤 = 𝐴 ↔ 𝑦 = 𝐴 ) )
3	1 2	sbievw2	⊢ ( [ 𝑦 / 𝑥 ] 𝑥 = 𝐴 ↔ 𝑦 = 𝐴 )