Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > cnveqd | Structured version Visualization version GIF version |
Description: Equality deduction for converse relation. (Contributed by NM, 6-Dec-2013.) |
Ref | Expression |
---|---|
cnveqd.1 | ⊢ (𝜑 → 𝐴 = 𝐵) |
Ref | Expression |
---|---|
cnveqd | ⊢ (𝜑 → ◡𝐴 = ◡𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnveqd.1 | . 2 ⊢ (𝜑 → 𝐴 = 𝐵) | |
2 | cnveq 5710 | . 2 ⊢ (𝐴 = 𝐵 → ◡𝐴 = ◡𝐵) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → ◡𝐴 = ◡𝐵) |
Copyright terms: Public domain | W3C validator |