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Mirrors > Home > MPE Home > Th. List > nesymir | Structured version Visualization version GIF version |
Description: Inference associated with nesym 3072. (Contributed by BJ, 7-Jul-2018.) (Proof shortened by Wolf Lammen, 25-Nov-2019.) |
Ref | Expression |
---|---|
nesymir.1 | ⊢ ¬ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
nesymir | ⊢ 𝐵 ≠ 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nesymir.1 | . . 3 ⊢ ¬ 𝐴 = 𝐵 | |
2 | 1 | neir 3019 | . 2 ⊢ 𝐴 ≠ 𝐵 |
3 | 2 | necomi 3070 | 1 ⊢ 𝐵 ≠ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 = wceq 1528 ≠ wne 3016 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-9 2115 ax-ext 2793 |
This theorem depends on definitions: df-bi 208 df-an 397 df-ex 1772 df-cleq 2814 df-ne 3017 |
This theorem is referenced by: relowlpssretop 34528 |
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