Metamath Proof Explorer

Theorem ltnegd

Description: Negative of both sides of 'less than'. Theorem I.23 of Apostol p. 20. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses leidd.1 φ A
ltnegd.2 φ B
Assertion ltnegd φ A < B B < A


Step Hyp Ref Expression
1 leidd.1 φ A
2 ltnegd.2 φ B
3 ltneg A B A < B B < A
4 1 2 3 syl2anc φ A < B B < A