Metamath Proof Explorer


Theorem xreqled

Description: Equality implies 'less than or equal to'. (Contributed by Glauco Siliprandi, 17-Aug-2020)

Ref Expression
Hypotheses xreqled.1 ( 𝜑𝐴 ∈ ℝ* )
xreqled.2 ( 𝜑𝐴 = 𝐵 )
Assertion xreqled ( 𝜑𝐴𝐵 )

Proof

Step Hyp Ref Expression
1 xreqled.1 ( 𝜑𝐴 ∈ ℝ* )
2 xreqled.2 ( 𝜑𝐴 = 𝐵 )
3 xreqle ( ( 𝐴 ∈ ℝ*𝐴 = 𝐵 ) → 𝐴𝐵 )
4 1 2 3 syl2anc ( 𝜑𝐴𝐵 )