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Mirrors > Home > ILE Home > Th. List > nesymi | GIF version |
Description: Inference associated with nesym 2250. (Contributed by BJ, 7-Jul-2018.) |
Ref | Expression |
---|---|
nesymi.1 | ⊢ 𝐴 ≠ 𝐵 |
Ref | Expression |
---|---|
nesymi | ⊢ ¬ 𝐵 = 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nesymi.1 | . 2 ⊢ 𝐴 ≠ 𝐵 | |
2 | nesym 2250 | . 2 ⊢ (𝐴 ≠ 𝐵 ↔ ¬ 𝐵 = 𝐴) | |
3 | 1, 2 | mpbi 133 | 1 ⊢ ¬ 𝐵 = 𝐴 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 = wceq 1243 ≠ wne 2204 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-5 1336 ax-gen 1338 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-cleq 2033 df-ne 2206 |
This theorem is referenced by: frec0g 5983 xrltnr 8701 nltmnf 8709 |
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