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Mirrors > Home > MPE Home > Th. List > df2o3 | Structured version Visualization version Unicode version |
Description: Expanded value of the ordinal number 2. (Contributed by Mario Carneiro, 14-Aug-2015.) |
Ref | Expression |
---|---|
df2o3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2o 7561 | . 2 | |
2 | df-suc 5729 | . 2 | |
3 | df1o2 7572 | . . . 4 | |
4 | 3 | uneq1i 3763 | . . 3 |
5 | df-pr 4180 | . . 3 | |
6 | 4, 5 | eqtr4i 2647 | . 2 |
7 | 1, 2, 6 | 3eqtri 2648 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 cun 3572 c0 3915 csn 4177 cpr 4179 csuc 5725 c1o 7553 c2o 7554 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-dif 3577 df-un 3579 df-nul 3916 df-pr 4180 df-suc 5729 df-1o 7560 df-2o 7561 |
This theorem is referenced by: df2o2 7574 2oconcl 7583 map2xp 8130 1sdom 8163 cantnflem2 8587 xp2cda 9002 sdom2en01 9124 sadcf 15175 xpscfn 16219 xpscfv 16222 xpsfrnel 16223 xpsfeq 16224 xpsfrnel2 16225 xpsle 16241 setcepi 16738 efgi0 18133 efgi1 18134 vrgpf 18181 vrgpinv 18182 frgpuptinv 18184 frgpup2 18189 frgpup3lem 18190 frgpnabllem1 18276 dmdprdpr 18448 dprdpr 18449 xpstopnlem1 21612 xpstopnlem2 21614 xpsxmetlem 22184 xpsdsval 22186 xpsmet 22187 onint1 32448 pw2f1ocnv 37604 wepwsolem 37612 df3o2 38322 clsk1independent 38344 |
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