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Mirrors > Home > ILE Home > Th. List > nesymir | GIF version |
Description: Inference associated with nesym 2392. (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 2392 | . 2 ⊢ (𝐵 ≠ 𝐴 ↔ ¬ 𝐴 = 𝐵) | |
3 | 1, 2 | mpbir 146 | 1 ⊢ 𝐵 ≠ 𝐴 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 = wceq 1353 ≠ wne 2347 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-5 1447 ax-gen 1449 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-cleq 2170 df-ne 2348 |
This theorem is referenced by: (None) |
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