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 Description: Equality inference for cardinal addition. (Contributed by SF, 3-Feb-2015.)
Hypothesis
Ref Expression
Assertion
Ref Expression
addceq2i (C +c A) = (C +c B)

StepHypRef Expression
1 addceqi.1 . 2 A = B
2 addceq2 4384 . 2 (A = B → (C +c A) = (C +c B))
31, 2ax-mp 5 1 (C +c A) = (C +c B)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642   +c cplc 4375 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334  ax-nin 4078  ax-sn 4087 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-rex 2620  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-symdif 3216  df-ss 3259  df-nul 3551  df-pw 3724  df-sn 3741  df-pr 3742  df-opk 4058  df-1c 4136  df-pw1 4137  df-ins2k 4187  df-ins3k 4188  df-imak 4189  df-sik 4192  df-ssetk 4193  df-addc 4378 This theorem is referenced by:  addcid1  4405  addc32  4416  nmembers1  6271  nncdiv3  6277  nnc3n3p2  6279  nnc3p1n3p2  6280  nchoicelem1  6289  nchoicelem2  6290  nchoicelem17  6305
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