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Mirrors > Home > MPE Home > Th. List > ltpiord | Structured version Visualization version Unicode version |
Description: Positive integer 'less than' in terms of ordinal membership. (Contributed by NM, 6-Feb-1996.) (Revised by Mario Carneiro, 28-Apr-2015.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ltpiord |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-lti 9305 |
. . 3
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2 | 1 | breqi 4411 |
. 2
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3 | brinxp 4900 |
. . 3
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4 | epelg 4749 |
. . . 4
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5 | 4 | adantl 468 |
. . 3
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6 | 3, 5 | bitr3d 259 |
. 2
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7 | 2, 6 | syl5bb 261 |
1
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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 1671 ax-4 1684 ax-5 1760 ax-6 1807 ax-7 1853 ax-9 1898 ax-10 1917 ax-11 1922 ax-12 1935 ax-13 2093 ax-ext 2433 ax-sep 4528 ax-nul 4537 ax-pr 4642 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 988 df-tru 1449 df-ex 1666 df-nf 1670 df-sb 1800 df-eu 2305 df-mo 2306 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2583 df-ne 2626 df-ral 2744 df-rex 2745 df-rab 2748 df-v 3049 df-dif 3409 df-un 3411 df-in 3413 df-ss 3420 df-nul 3734 df-if 3884 df-sn 3971 df-pr 3973 df-op 3977 df-br 4406 df-opab 4465 df-eprel 4748 df-xp 4843 df-lti 9305 |
This theorem is referenced by: ltexpi 9332 ltapi 9333 ltmpi 9334 1lt2pi 9335 nlt1pi 9336 indpi 9337 nqereu 9359 |
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