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Theorem addid2d 7143
Description: 0 is a left identity for addition. (Contributed by Mario Carneiro, 27-May-2016.)
Hypothesis
Ref Expression
muld.1 (𝜑𝐴 ∈ ℂ)
Assertion
Ref Expression
addid2d (𝜑 → (0 + 𝐴) = 𝐴)

Proof of Theorem addid2d
StepHypRef Expression
1 muld.1 . 2 (𝜑𝐴 ∈ ℂ)
2 addid2 7132 . 2 (𝐴 ∈ ℂ → (0 + 𝐴) = 𝐴)
31, 2syl 14 1 (𝜑 → (0 + 𝐴) = 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1243  wcel 1393  (class class class)co 5499  cc 6868  0cc0 6870   + caddc 6873
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-ext 2022  ax-1cn 6958  ax-icn 6960  ax-addcl 6961  ax-mulcl 6963  ax-addcom 6965  ax-i2m1 6970  ax-0id 6973
This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-clel 2036
This theorem is referenced by:  negeu  7182  ltadd2  7395  subge0  7448  un0addcl  8187  lincmb01cmp  8838  rennim  9478
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