Description: Substitution applied to an atomic wff (class version of equsb3 ). (Contributed by Rodolfo Medina, 28-Apr-2010)
Ref | Expression | ||
---|---|---|---|
Assertion | eqsb3 | ⊢ ( [ 𝑦 / 𝑥 ] 𝑥 = 𝐴 ↔ 𝑦 = 𝐴 ) |
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 ) |