Metamath Proof Explorer


Theorem eqleltd

Description: Equality in terms of 'less than or equal to', 'less than'. (Contributed by NM, 7-Apr-2001)

Ref Expression
Hypotheses ltd.1 φA
ltd.2 φB
Assertion eqleltd φA=BAB¬A<B

Proof

Step Hyp Ref Expression
1 ltd.1 φA
2 ltd.2 φB
3 eqlelt ABA=BAB¬A<B
4 1 2 3 syl2anc φA=BAB¬A<B