Description: Inference applying commutative law for class equality to an antecedent. (Contributed by NM, 24-Jun-1993)
Ref | Expression | ||
---|---|---|---|
Hypothesis | eqcoms.1 | ⊢ ( 𝐴 = 𝐵 → 𝜑 ) | |
Assertion | eqcoms | ⊢ ( 𝐵 = 𝐴 → 𝜑 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqcoms.1 | ⊢ ( 𝐴 = 𝐵 → 𝜑 ) | |
2 | eqcom | ⊢ ( 𝐵 = 𝐴 ↔ 𝐴 = 𝐵 ) | |
3 | 2 1 | sylbi | ⊢ ( 𝐵 = 𝐴 → 𝜑 ) |