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Metamath Proof Explorer

Theorem cxprecd

Description: Complex exponentiation of a reciprocal. (Contributed by Mario Carneiro, 30-May-2016)

Ref Expression
Hypotheses rpcxpcld.1 ⊢ φ → A ∈ ℝ +
cxprecd.2 ⊢ φ → B ∈ ℂ
Assertion cxprecd ⊢ φ → 1 A B = 1 A B

Proof

Step Hyp Ref Expression
1 rpcxpcld.1 ⊢ φ → A ∈ ℝ +
2 cxprecd.2 ⊢ φ → B ∈ ℂ
3 cxprec ⊢ A ∈ ℝ + ∧ B ∈ ℂ → 1 A B = 1 A B
4 1 2 3 syl2anc ⊢ φ → 1 A B = 1 A B