| Colors of
variables: wff
setvar class |
| Syntax hints:
→ wi 4 ∧ wa 395
= wceq 1534 ∈
wcel 2099 {crab 3429
⊆ wss 3947 {csn 4629
∩ cint 4949
× cxp 5676 “
cima 5681 Oncon0 6369
(class class class)co 7420 +no cnadd 8686 |
| This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906
ax-6 1964 ax-7 2004 ax-8 2101
ax-9 2109 ax-10 2130 ax-11 2147 ax-12 2167 ax-ext 2699 ax-rep 5285 ax-sep 5299 ax-nul 5306 ax-pow 5365 ax-pr 5429 ax-un 7740 |
| This theorem depends on definitions:
df-bi 206 df-an 396
df-or 847 df-3or 1086 df-3an 1087 df-tru 1537 df-fal 1547 df-ex 1775 df-nf 1779 df-sb 2061 df-mo 2530 df-eu 2559 df-clab 2706 df-cleq 2720 df-clel 2806 df-nfc 2881 df-ne 2938 df-ral 3059 df-rex 3068 df-reu 3374 df-rab 3430 df-v 3473 df-sbc 3777 df-csb 3893 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-pss 3966 df-nul 4324 df-if 4530 df-pw 4605 df-sn 4630 df-pr 4632 df-op 4636 df-uni 4909 df-int 4950 df-iun 4998 df-br 5149 df-opab 5211 df-mpt 5232 df-tr 5266 df-id 5576 df-eprel 5582 df-po 5590 df-so 5591 df-fr 5633 df-se 5634 df-we 5635 df-xp 5684 df-rel 5685 df-cnv 5686 df-co 5687 df-dm 5688 df-rn 5689 df-res 5690 df-ima 5691 df-pred 6305 df-ord 6372 df-on 6373 df-suc 6375 df-iota 6500 df-fun 6550 df-fn 6551 df-f 6552 df-f1 6553 df-fo 6554 df-f1o 6555 df-fv 6556 df-ov 7423 df-oprab 7424 df-mpo 7425 df-1st 7993 df-2nd 7994 df-frecs 8287 df-nadd 8687 |
| This theorem is referenced by: naddf
8702 naddssim
8706 naddel1
8708 naddss1
8710 naddasslem1
8715 naddasslem2
8716 nadd4
8719 naddel12
8721 addsproplem2
27900 addsprop
27906 mulsproplem5
28033 mulsproplem6
28034 mulsproplem7
28035 mulsproplem8
28036 mulsprop
28043 naddsuc2
42822 naddass1
42823 naddgeoa
42824 naddwordnexlem4
42831 |
