![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
Mirrors > Home > MPE Home > Th. List > onssnel2i | Structured version Unicode version |
Description: An ordering law for ordinal numbers. (Contributed by NM, 13-Jun-1994.) |
Ref | Expression |
---|---|
on.1 |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
onssnel2i |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | on.1 |
. . 3
![]() ![]() ![]() ![]() | |
2 | 1 | onirri 4923 |
. 2
![]() ![]() ![]() ![]() ![]() |
3 | ssel 3448 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 2, 3 | mtoi 178 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 ax-sep 4511 ax-nul 4519 ax-pr 4629 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2264 df-mo 2265 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ne 2646 df-ral 2800 df-rex 2801 df-rab 2804 df-v 3070 df-sbc 3285 df-dif 3429 df-un 3431 df-in 3433 df-ss 3440 df-nul 3736 df-if 3890 df-sn 3976 df-pr 3978 df-op 3982 df-uni 4190 df-br 4391 df-opab 4449 df-tr 4484 df-eprel 4730 df-po 4739 df-so 4740 df-fr 4777 df-we 4779 df-ord 4820 df-on 4821 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |