Description: Equality theorem for equivalence class (deduction form). (Contributed by Jim Kingdon, 31-Dec-2019)
Ref | Expression | ||
---|---|---|---|
Hypothesis | eceq1d.1 | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) | |
Assertion | eceq1d | ⊢ ( 𝜑 → [ 𝐴 ] 𝐶 = [ 𝐵 ] 𝐶 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eceq1d.1 | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) | |
2 | eceq1 | ⊢ ( 𝐴 = 𝐵 → [ 𝐴 ] 𝐶 = [ 𝐵 ] 𝐶 ) | |
3 | 1 2 | syl | ⊢ ( 𝜑 → [ 𝐴 ] 𝐶 = [ 𝐵 ] 𝐶 ) |