Description: A membership and equality inference. (Contributed by NM, 4-Jan-2006)
Ref | Expression | ||
---|---|---|---|
Hypotheses | eleqtrdi.1 | ⊢ ( 𝜑 → 𝐴 ∈ 𝐵 ) | |
eleqtrdi.2 | ⊢ 𝐵 = 𝐶 | ||
Assertion | eleqtrdi | ⊢ ( 𝜑 → 𝐴 ∈ 𝐶 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleqtrdi.1 | ⊢ ( 𝜑 → 𝐴 ∈ 𝐵 ) | |
2 | eleqtrdi.2 | ⊢ 𝐵 = 𝐶 | |
3 | 2 | a1i | ⊢ ( 𝜑 → 𝐵 = 𝐶 ) |
4 | 1 3 | eleqtrd | ⊢ ( 𝜑 → 𝐴 ∈ 𝐶 ) |