Metamath Proof Explorer


Theorem min2d

Description: The minimum of two numbers is less than or equal to the second. (Contributed by Glauco Siliprandi, 5-Feb-2022)

Ref Expression
Hypotheses min2d.1 φA
min2d.2 φB
Assertion min2d φifABABB

Proof

Step Hyp Ref Expression
1 min2d.1 φA
2 min2d.2 φB
3 min2 ABifABABB
4 1 2 3 syl2anc φifABABB