| Colors of
variables: wff
setvar class |
| Syntax hints:
→ wi 4 ∧ wa 395
= wceq 1533 ∈
wcel 2098 {crab 3424
⊆ wss 3941 {csn 4621
∩ cint 4941
× cxp 5665 “
cima 5670 Oncon0 6355
(class class class)co 7402 +no cnadd 8661 |
| This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905
ax-6 1963 ax-7 2003 ax-8 2100
ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2163 ax-ext 2695 ax-rep 5276 ax-sep 5290 ax-nul 5297 ax-pow 5354 ax-pr 5418 ax-un 7719 |
| This theorem depends on definitions:
df-bi 206 df-an 396
df-or 845 df-3or 1085 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2526 df-eu 2555 df-clab 2702 df-cleq 2716 df-clel 2802 df-nfc 2877 df-ne 2933 df-ral 3054 df-rex 3063 df-reu 3369 df-rab 3425 df-v 3468 df-sbc 3771 df-csb 3887 df-dif 3944 df-un 3946 df-in 3948 df-ss 3958 df-pss 3960 df-nul 4316 df-if 4522 df-pw 4597 df-sn 4622 df-pr 4624 df-op 4628 df-uni 4901 df-int 4942 df-iun 4990 df-br 5140 df-opab 5202 df-mpt 5223 df-tr 5257 df-id 5565 df-eprel 5571 df-po 5579 df-so 5580 df-fr 5622 df-se 5623 df-we 5624 df-xp 5673 df-rel 5674 df-cnv 5675 df-co 5676 df-dm 5677 df-rn 5678 df-res 5679 df-ima 5680 df-pred 6291 df-ord 6358 df-on 6359 df-suc 6361 df-iota 6486 df-fun 6536 df-fn 6537 df-f 6538 df-f1 6539 df-fo 6540 df-f1o 6541 df-fv 6542 df-ov 7405 df-oprab 7406 df-mpo 7407 df-1st 7969 df-2nd 7970 df-frecs 8262 df-nadd 8662 |
| This theorem is referenced by: naddf
8677 naddssim
8681 naddel1
8683 naddss1
8685 naddasslem1
8690 naddasslem2
8691 nadd4
8694 naddel12
8696 addsproplem2
27828 addsprop
27834 mulsproplem5
27961 mulsproplem6
27962 mulsproplem7
27963 mulsproplem8
27964 mulsprop
27971 naddsuc2
42693 naddass1
42694 naddgeoa
42695 naddwordnexlem4
42702 |
