| Colors of
variables: wff
setvar class |
| Syntax hints:
→ wi 4 ∧ wa 397
= wceq 1542 ∈
wcel 2107 {crab 3433
⊆ wss 3949 {csn 4629
∩ cint 4951
× cxp 5675 “
cima 5680 Oncon0 6365
(class class class)co 7409 +no cnadd 8664 |
| This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914
ax-6 1972 ax-7 2012 ax-8 2109
ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 ax-rep 5286 ax-sep 5300 ax-nul 5307 ax-pow 5364 ax-pr 5428 ax-un 7725 |
| This theorem depends on definitions:
df-bi 206 df-an 398
df-or 847 df-3or 1089 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ne 2942 df-ral 3063 df-rex 3072 df-reu 3378 df-rab 3434 df-v 3477 df-sbc 3779 df-csb 3895 df-dif 3952 df-un 3954 df-in 3956 df-ss 3966 df-pss 3968 df-nul 4324 df-if 4530 df-pw 4605 df-sn 4630 df-pr 4632 df-op 4636 df-uni 4910 df-int 4952 df-iun 5000 df-br 5150 df-opab 5212 df-mpt 5233 df-tr 5267 df-id 5575 df-eprel 5581 df-po 5589 df-so 5590 df-fr 5632 df-se 5633 df-we 5634 df-xp 5683 df-rel 5684 df-cnv 5685 df-co 5686 df-dm 5687 df-rn 5688 df-res 5689 df-ima 5690 df-pred 6301 df-ord 6368 df-on 6369 df-suc 6371 df-iota 6496 df-fun 6546 df-fn 6547 df-f 6548 df-f1 6549 df-fo 6550 df-f1o 6551 df-fv 6552 df-ov 7412 df-oprab 7413 df-mpo 7414 df-1st 7975 df-2nd 7976 df-frecs 8266 df-nadd 8665 |
| This theorem is referenced by: naddf
8680 naddssim
8684 naddel1
8686 naddss1
8688 naddasslem1
8693 naddasslem2
8694 nadd4
8697 naddel12
8699 addsproplem2
27454 addsprop
27460 mulsproplem5
27576 mulsproplem6
27577 mulsproplem7
27578 mulsproplem8
27579 mulsprop
27586 naddsuc2
42143 naddass1
42144 naddgeoa
42145 naddwordnexlem4
42152 |
