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Theorem mulid2d 6823
Description: Identity law for multiplication. (Contributed by Mario Carneiro, 27-May-2016.)
Hypothesis
Ref Expression
addcld.1 (φA ℂ)
Assertion
Ref Expression
mulid2d (φ → (1 · A) = A)

Proof of Theorem mulid2d
StepHypRef Expression
1 addcld.1 . 2 (φA ℂ)
2 mulid2 6803 . 2 (A ℂ → (1 · A) = A)
31, 2syl 14 1 (φ → (1 · A) = A)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242   wcel 1390  (class class class)co 5455  cc 6689  1c1 6692   · cmul 6696
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-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-resscn 6755  ax-1cn 6756  ax-icn 6758  ax-addcl 6759  ax-mulcl 6761  ax-mulcom 6764  ax-mulass 6766  ax-distr 6767  ax-1rid 6770  ax-cnre 6774
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-sn 3373  df-pr 3374  df-op 3376  df-uni 3572  df-br 3756  df-iota 4810  df-fv 4853  df-ov 5458
This theorem is referenced by:  mulsubfacd  7191  mulcanapd  7404  receuap  7412  divdivdivap  7451  divcanap5  7452  ltrec  7610  recp1lt1  7626  nndivtr  7716  gtndiv  8091  lincmb01cmp  8621  iccf1o  8622  m1expcl2  8911  expgt1  8927  ltexp2a  8940  leexp2a  8941  binom3  8999
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