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Mirrors > Home > MPE Home > Th. List > pleval2 | Structured version Visualization version Unicode version |
Description: Less-than-or-equal in terms of less-than. (sspss 3518 analog.) (Contributed by NM, 17-Oct-2011.) (Revised by Mario Carneiro, 8-Feb-2015.) |
Ref | Expression |
---|---|
pleval2.b |
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pleval2.l |
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pleval2.s |
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Ref | Expression |
---|---|
pleval2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pleval2.b |
. . . 4
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2 | pleval2.l |
. . . 4
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3 | pleval2.s |
. . . 4
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4 | 1, 2, 3 | pleval2i 16288 |
. . 3
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5 | 4 | 3adant1 1048 |
. 2
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6 | 2, 3 | pltle 16285 |
. . 3
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7 | 1, 2 | posref 16274 |
. . . . 5
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8 | 7 | 3adant3 1050 |
. . . 4
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9 | breq2 4399 |
. . . 4
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10 | 8, 9 | syl5ibcom 228 |
. . 3
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11 | 6, 10 | jaod 387 |
. 2
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12 | 5, 11 | impbid 195 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-8 1906 ax-9 1913 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 ax-sep 4518 ax-nul 4527 ax-pow 4579 ax-pr 4639 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3an 1009 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-eu 2323 df-mo 2324 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-ne 2643 df-ral 2761 df-rex 2762 df-rab 2765 df-v 3033 df-sbc 3256 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-nul 3723 df-if 3873 df-sn 3960 df-pr 3962 df-op 3966 df-uni 4191 df-br 4396 df-opab 4455 df-mpt 4456 df-id 4754 df-xp 4845 df-rel 4846 df-cnv 4847 df-co 4848 df-dm 4849 df-iota 5553 df-fun 5591 df-fv 5597 df-preset 16251 df-poset 16269 df-plt 16282 |
This theorem is referenced by: pltletr 16295 plelttr 16296 tosso 16360 tlt3 28501 orngsqr 28641 |
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