Description: An equality transitivity deduction. (Contributed by NM, 29-Mar-1998)
Ref | Expression | ||
---|---|---|---|
Hypotheses | syl6reqr.1 | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) | |
syl6reqr.2 | ⊢ 𝐶 = 𝐵 | ||
Assertion | syl6reqr | ⊢ ( 𝜑 → 𝐶 = 𝐴 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl6reqr.1 | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) | |
2 | syl6reqr.2 | ⊢ 𝐶 = 𝐵 | |
3 | 2 | eqcomi | ⊢ 𝐵 = 𝐶 |
4 | 1 3 | syl6req | ⊢ ( 𝜑 → 𝐶 = 𝐴 ) |