Theorem addcid2 4407

Description: Cardinal zero is a fixed point for cardinal addition. Theorem X.1.8 of [Rosser] p. 276. (Contributed by SF, 16-Jan-2015.)

Assertion

Ref	Expression
addcid2	|- (0c +o A) = A

Proof of Theorem addcid2

Step	Hyp	Ref	Expression
1		addccom 4406	. 2 |- (0c +o A) = (A +o 0c)
2		addcid1 4405	. 2 |- (A +o 0c) = A
3	1, 2	eqtri 2373	1 |- (0c +o A) = A

Syntax hints:   = wceq 1642  0_cc0c 4374   +o 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-ral 2619  df-rex 2620  df-v 2861  df-sbc 3047  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-0c 4377  df-addc 4378

This theorem is referenced by:  nnsucelr  4428  preaddccan2  4455  0cminle  4461  tfin1c  4499  0ceven  4505  evenodddisj  4516  addceq0  6219  1ne0c  6241  addccan2nc  6265  nncdiv3  6277  nnc3n3p1  6278  nchoicelem14  6302  nchoicelem17  6305