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Metamath Proof Explorer

Theorem eqled

Description: Equality implies 'less than or equal to'. (Contributed by Glauco Siliprandi, 11-Dec-2019)

Ref Expression
Hypotheses eqled.1 ⊢ φ → A ∈ ℝ
eqled.2 ⊢ φ → A = B
Assertion eqled ⊢ φ → A ≤ B

Proof

Step Hyp Ref Expression
1 eqled.1 ⊢ φ → A ∈ ℝ
2 eqled.2 ⊢ φ → A = B
3 eqle ⊢ A ∈ ℝ ∧ A = B → A ≤ B
4 1 2 3 syl2anc ⊢ φ → A ≤ B