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Mirrors > Home > NFE Home > Th. List > addceq12 | Unicode version |
Description: Equality law for cardinal addition. (Contributed by SF, 15-Jan-2015.) |
Ref | Expression |
---|---|
addceq12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | addceq1 4383 | . 2 | |
2 | addceq2 4384 | . 2 | |
3 | 1, 2 | sylan9eq 2405 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 358 wceq 1642 cplc 4375 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 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: addceq12i 4388 addceq12d 4391 0ceven 4505 sucoddeven 4511 evenodddisj 4516 eventfin 4517 oddtfin 4518 sfintfin 4532 ncaddccl 6144 tcdi 6164 ce0addcnnul 6179 addceq0 6219 letc 6231 addcdi 6250 nncdiv3 6277 nnc3n3p1 6278 |
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