Description: An equality transitivity deduction. (Contributed by NM, 21-Jun-1993)
Ref | Expression | ||
---|---|---|---|
Hypotheses | syl5eq.1 | ⊢ 𝐴 = 𝐵 | |
syl5eq.2 | ⊢ ( 𝜑 → 𝐵 = 𝐶 ) | ||
Assertion | syl5eq | ⊢ ( 𝜑 → 𝐴 = 𝐶 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl5eq.1 | ⊢ 𝐴 = 𝐵 | |
2 | syl5eq.2 | ⊢ ( 𝜑 → 𝐵 = 𝐶 ) | |
3 | 1 | a1i | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) |
4 | 3 2 | eqtrd | ⊢ ( 𝜑 → 𝐴 = 𝐶 ) |