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Mirrors > Home > MPE Home > Th. List > alephord2i | Unicode version |
Description: Ordering property of the aleph function. Theorem 66 of [Suppes] p. 229. (Contributed by NM, 25-Oct-2003.) |
Ref | Expression |
---|---|
alephord2i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | onelon 4566 |
. . 3
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2 | alephord2 7913 |
. . . . 5
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3 | 2 | biimpd 199 |
. . . 4
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4 | 3 | expimpd 587 |
. . 3
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5 | 1, 4 | mpcom 34 |
. 2
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6 | 5 | ex 424 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem is referenced by: alephle 7925 alephsmo 7939 alephfp 7945 alephval3 7947 alephsing 8112 pwcfsdom 8414 winalim2 8527 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1552 ax-5 1563 ax-17 1623 ax-9 1662 ax-8 1683 ax-13 1723 ax-14 1725 ax-6 1740 ax-7 1745 ax-11 1757 ax-12 1946 ax-ext 2385 ax-rep 4280 ax-sep 4290 ax-nul 4298 ax-pow 4337 ax-pr 4363 ax-un 4660 ax-inf2 7552 |
This theorem depends on definitions: df-bi 178 df-or 360 df-an 361 df-3or 937 df-3an 938 df-tru 1325 df-ex 1548 df-nf 1551 df-sb 1656 df-eu 2258 df-mo 2259 df-clab 2391 df-cleq 2397 df-clel 2400 df-nfc 2529 df-ne 2569 df-ral 2671 df-rex 2672 df-reu 2673 df-rmo 2674 df-rab 2675 df-v 2918 df-sbc 3122 df-csb 3212 df-dif 3283 df-un 3285 df-in 3287 df-ss 3294 df-pss 3296 df-nul 3589 df-if 3700 df-pw 3761 df-sn 3780 df-pr 3781 df-tp 3782 df-op 3783 df-uni 3976 df-int 4011 df-iun 4055 df-br 4173 df-opab 4227 df-mpt 4228 df-tr 4263 df-eprel 4454 df-id 4458 df-po 4463 df-so 4464 df-fr 4501 df-se 4502 df-we 4503 df-ord 4544 df-on 4545 df-lim 4546 df-suc 4547 df-om 4805 df-xp 4843 df-rel 4844 df-cnv 4845 df-co 4846 df-dm 4847 df-rn 4848 df-res 4849 df-ima 4850 df-iota 5377 df-fun 5415 df-fn 5416 df-f 5417 df-f1 5418 df-fo 5419 df-f1o 5420 df-fv 5421 df-isom 5422 df-riota 6508 df-recs 6592 df-rdg 6627 df-er 6864 df-en 7069 df-dom 7070 df-sdom 7071 df-fin 7072 df-oi 7435 df-har 7482 df-card 7782 df-aleph 7783 |
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