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Mirrors > Home > MPE Home > Th. List > 2lt4 | Structured version Unicode version |
Description: 2 is less than 4. (Contributed by Mario Carneiro, 15-Sep-2013.) |
Ref | Expression |
---|---|
2lt4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2lt3 10590 |
. 2
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2 | 3lt4 10592 |
. 2
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3 | 2re 10492 |
. . 3
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4 | 3re 10496 |
. . 3
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5 | 4re 10499 |
. . 3
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6 | 3, 4, 5 | lttri 9601 |
. 2
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7 | 1, 2, 6 | mp2an 672 |
1
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Colors of variables: wff setvar class |
Syntax hints: class class
class wbr 4390 ![]() ![]() ![]() ![]() |
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-8 1760 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-pow 4568 ax-pr 4629 ax-un 6472 ax-resscn 9440 ax-1cn 9441 ax-icn 9442 ax-addcl 9443 ax-addrcl 9444 ax-mulcl 9445 ax-mulrcl 9446 ax-mulcom 9447 ax-addass 9448 ax-mulass 9449 ax-distr 9450 ax-i2m1 9451 ax-1ne0 9452 ax-1rid 9453 ax-rnegex 9454 ax-rrecex 9455 ax-cnre 9456 ax-pre-lttri 9457 ax-pre-lttrn 9458 ax-pre-ltadd 9459 ax-pre-mulgt0 9460 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3or 966 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-nel 2647 df-ral 2800 df-rex 2801 df-reu 2802 df-rab 2804 df-v 3070 df-sbc 3285 df-csb 3387 df-dif 3429 df-un 3431 df-in 3433 df-ss 3440 df-nul 3736 df-if 3890 df-pw 3960 df-sn 3976 df-pr 3978 df-op 3982 df-uni 4190 df-br 4391 df-opab 4449 df-mpt 4450 df-id 4734 df-po 4739 df-so 4740 df-xp 4944 df-rel 4945 df-cnv 4946 df-co 4947 df-dm 4948 df-rn 4949 df-res 4950 df-ima 4951 df-iota 5479 df-fun 5518 df-fn 5519 df-f 5520 df-f1 5521 df-fo 5522 df-f1o 5523 df-fv 5524 df-riota 6151 df-ov 6193 df-oprab 6194 df-mpt2 6195 df-er 7201 df-en 7411 df-dom 7412 df-sdom 7413 df-pnf 9521 df-mnf 9522 df-xr 9523 df-ltxr 9524 df-le 9525 df-sub 9698 df-neg 9699 df-2 10481 df-3 10482 df-4 10483 |
This theorem is referenced by: 1lt4 10594 2lt5 10597 fzo0to42pr 11717 sqr2gt1lt2 12866 cos01bnd 13572 4sqlem12 14119 prdsvalstr 14493 pcoass 20712 pilem3 22034 ppiublem1 22657 bpos1 22738 2sqlem11 22830 usgraexvlem 23448 usgraex2elv 23451 4cycl4v4e 23687 4cycl4dv 23688 sqsscirc1 26472 4bc2eq6 27525 hlhilsplus 35894 |
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