Description: An equality transitivity equality deduction. (Contributed by NM, 18-Jul-1995)
Ref | Expression | ||
---|---|---|---|
Hypotheses | eqtr4d.1 | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) | |
eqtr4d.2 | ⊢ ( 𝜑 → 𝐶 = 𝐵 ) | ||
Assertion | eqtr4d | ⊢ ( 𝜑 → 𝐴 = 𝐶 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqtr4d.1 | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) | |
2 | eqtr4d.2 | ⊢ ( 𝜑 → 𝐶 = 𝐵 ) | |
3 | 2 | eqcomd | ⊢ ( 𝜑 → 𝐵 = 𝐶 ) |
4 | 1 3 | eqtrd | ⊢ ( 𝜑 → 𝐴 = 𝐶 ) |