Description: An equality transitivity deduction. (Contributed by NM, 21-Jun-1993)
Ref | Expression | ||
---|---|---|---|
Hypotheses | syl6eq.1 | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) | |
syl6eq.2 | ⊢ 𝐵 = 𝐶 | ||
Assertion | syl6eq | ⊢ ( 𝜑 → 𝐴 = 𝐶 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl6eq.1 | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) | |
2 | syl6eq.2 | ⊢ 𝐵 = 𝐶 | |
3 | 2 | a1i | ⊢ ( 𝜑 → 𝐵 = 𝐶 ) |
4 | 1 3 | eqtrd | ⊢ ( 𝜑 → 𝐴 = 𝐶 ) |