Metamath Proof Explorer


Theorem max1ALT

Description: A number is less than or equal to the maximum of it and another. This version of max1 omits the B e. RR antecedent. Although it doesn't exploit undefined behavior, it is still considered poor style, and the use of max1 is preferred. (Proof modification is discouraged.) (New usage is discouraged.) (Contributed by NM, 3-Apr-2005)

Ref Expression
Assertion max1ALT AAifABBA

Proof

Step Hyp Ref Expression
1 leid AAA
2 iffalse ¬ABifABBA=A
3 2 breq2d ¬ABAifABBAAA
4 1 3 syl5ibrcom A¬ABAifABBA
5 id ABAB
6 iftrue ABifABBA=B
7 5 6 breqtrrd ABAifABBA
8 4 7 pm2.61d2 AAifABBA