pub theorem axext (a b: nat): $ a == b -> a = b $;
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssle | a C_ b -> a <= b |
|
2 | eqss | a == b -> a C_ b |
|
3 | 1, 2 | syl | a == b -> a <= b |
4 | ssle | b C_ a -> b <= a |
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5 | eqssr | a == b -> b C_ a |
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6 | 4, 5 | syl | a == b -> b <= a |
7 | 3, 6 | leasymd | a == b -> a = b |