Description: A membership and equality inference. (Contributed by NM, 4-Jan-2006)
Ref | Expression | ||
---|---|---|---|
Hypotheses | syl6eqelr.1 | ⊢ ( 𝜑 → 𝐵 = 𝐴 ) | |
syl6eqelr.2 | ⊢ 𝐵 ∈ 𝐶 | ||
Assertion | syl6eqelr | ⊢ ( 𝜑 → 𝐴 ∈ 𝐶 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl6eqelr.1 | ⊢ ( 𝜑 → 𝐵 = 𝐴 ) | |
2 | syl6eqelr.2 | ⊢ 𝐵 ∈ 𝐶 | |
3 | 1 | eqcomd | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) |
4 | 3 2 | syl6eqel | ⊢ ( 𝜑 → 𝐴 ∈ 𝐶 ) |