![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > syl6eleqr | GIF version |
Description: A membership and equality inference. (Contributed by NM, 24-Apr-2005.) |
Ref | Expression |
---|---|
syl6eleqr.1 | ⊢ (𝜑 → 𝐴 ∈ 𝐵) |
syl6eleqr.2 | ⊢ 𝐶 = 𝐵 |
Ref | Expression |
---|---|
syl6eleqr | ⊢ (𝜑 → 𝐴 ∈ 𝐶) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl6eleqr.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ 𝐵) | |
2 | syl6eleqr.2 | . . 3 ⊢ 𝐶 = 𝐵 | |
3 | 2 | eqcomi 2104 | . 2 ⊢ 𝐵 = 𝐶 |
4 | 1, 3 | syl6eleq 2192 | 1 ⊢ (𝜑 → 𝐴 ∈ 𝐶) |
Copyright terms: Public domain | W3C validator |