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Mirrors > Home > ILE Home > Th. List > nesymir | GIF version |
Description: Inference associated with nesym 2290. (Contributed by BJ, 7-Jul-2018.) |
Ref | Expression |
---|---|
nesymir.1 | ⊢ ¬ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
nesymir | ⊢ 𝐵 ≠ 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nesymir.1 | . 2 ⊢ ¬ 𝐴 = 𝐵 | |
2 | nesym 2290 | . 2 ⊢ (𝐵 ≠ 𝐴 ↔ ¬ 𝐴 = 𝐵) | |
3 | 1, 2 | mpbir 144 | 1 ⊢ 𝐵 ≠ 𝐴 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 = wceq 1284 ≠ wne 2245 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-5 1376 ax-gen 1378 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-cleq 2074 df-ne 2246 |
This theorem is referenced by: (None) |
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