Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > nesymi | GIF version |
Description: Inference associated with nesym 2353. (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 2353 | . 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 2308 |
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 2121 |
This theorem depends on definitions: df-bi 116 df-cleq 2132 df-ne 2309 |
This theorem is referenced by: frec0g 6294 djune 6963 omp1eomlem 6979 fodjum 7018 fodju0 7019 ismkvnex 7029 mkvprop 7032 xrltnr 9566 nltmnf 9574 xnn0xadd0 9650 pwle2 13193 nninfalllem1 13203 nninfall 13204 nninfsellemeq 13210 |
Copyright terms: Public domain | W3C validator |