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Mirrors > Home > ILE Home > Th. List > nesymi | GIF version |
Description: Inference associated with nesym 2351. (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 2351 | . 2 ⊢ (𝐴 ≠ 𝐵 ↔ ¬ 𝐵 = 𝐴) | |
3 | 1, 2 | mpbi 144 | 1 ⊢ ¬ 𝐵 = 𝐴 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 = wceq 1331 ≠ wne 2306 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 603 ax-in2 604 ax-5 1423 ax-gen 1425 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-cleq 2130 df-ne 2307 |
This theorem is referenced by: frec0g 6287 djune 6956 omp1eomlem 6972 fodjum 7011 fodju0 7012 ismkvnex 7022 mkvprop 7025 xrltnr 9559 nltmnf 9567 xnn0xadd0 9643 pwle2 13182 nninfalllem1 13192 nninfall 13193 nninfsellemeq 13199 |
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