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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 ⊢ ( 𝜑 → 𝐴 ∈ ℝ* )
xreqled.2 ⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion xreqled ( 𝜑 → 𝐴 ≤ 𝐵 )

Proof

Step Hyp Ref Expression
1 xreqled.1 ⊢ ( 𝜑 → 𝐴 ∈ ℝ* )
2 xreqled.2 ⊢ ( 𝜑 → 𝐴 = 𝐵 )
3 xreqle ⊢ ( ( 𝐴 ∈ ℝ* ∧ 𝐴 = 𝐵 ) → 𝐴 ≤ 𝐵 )
4 1 2 3 syl2anc ⊢ ( 𝜑 → 𝐴 ≤ 𝐵 )