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Metamath Proof Explorer

Theorem ltaddrpd

Description: Adding a positive number to another number increases it. (Contributed by Mario Carneiro, 28-May-2016)

Ref Expression
Hypotheses rpgecld.1 ⊢ φ → A ∈ ℝ
rpgecld.2 ⊢ φ → B ∈ ℝ +
Assertion ltaddrpd ⊢ φ → A < A + B

Proof

Step Hyp Ref Expression
1 rpgecld.1 ⊢ φ → A ∈ ℝ
2 rpgecld.2 ⊢ φ → B ∈ ℝ +
3 ltaddrp ⊢ A ∈ ℝ ∧ B ∈ ℝ + → A < A + B
4 1 2 3 syl2anc ⊢ φ → A < A + B