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Mirrors > Home > MPE Home > Th. List > ex-pss | Structured version Visualization version Unicode version |
Description: Example for df-pss 3432. Example by David A. Wheeler. (Contributed by Mario Carneiro, 6-May-2015.) |
Ref | Expression |
---|---|
ex-pss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ex-ss 25933 |
. 2
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2 | 3ex 10718 |
. . . . 5
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3 | 2 | tpid3 4101 |
. . . 4
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4 | 1re 9673 |
. . . . . 6
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5 | 1lt3 10812 |
. . . . . 6
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6 | 4, 5 | gtneii 9777 |
. . . . 5
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7 | 2re 10712 |
. . . . . 6
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8 | 2lt3 10811 |
. . . . . 6
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9 | 7, 8 | gtneii 9777 |
. . . . 5
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10 | 6, 9 | nelpri 4000 |
. . . 4
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11 | nelne1 2732 |
. . . 4
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12 | 3, 10, 11 | mp2an 683 |
. . 3
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13 | 12 | necomi 2690 |
. 2
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14 | df-pss 3432 |
. 2
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15 | 1, 13, 14 | mpbir2an 936 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-8 1900 ax-9 1907 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 ax-sep 4541 ax-nul 4550 ax-pow 4598 ax-pr 4656 ax-un 6615 ax-resscn 9627 ax-1cn 9628 ax-icn 9629 ax-addcl 9630 ax-addrcl 9631 ax-mulcl 9632 ax-mulrcl 9633 ax-mulcom 9634 ax-addass 9635 ax-mulass 9636 ax-distr 9637 ax-i2m1 9638 ax-1ne0 9639 ax-1rid 9640 ax-rnegex 9641 ax-rrecex 9642 ax-cnre 9643 ax-pre-lttri 9644 ax-pre-lttrn 9645 ax-pre-ltadd 9646 ax-pre-mulgt0 9647 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3or 992 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-eu 2314 df-mo 2315 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-nel 2636 df-ral 2754 df-rex 2755 df-reu 2756 df-rab 2758 df-v 3059 df-sbc 3280 df-csb 3376 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-pss 3432 df-nul 3744 df-if 3894 df-pw 3965 df-sn 3981 df-pr 3983 df-tp 3985 df-op 3987 df-uni 4213 df-br 4419 df-opab 4478 df-mpt 4479 df-id 4771 df-po 4777 df-so 4778 df-xp 4862 df-rel 4863 df-cnv 4864 df-co 4865 df-dm 4866 df-rn 4867 df-res 4868 df-ima 4869 df-iota 5569 df-fun 5607 df-fn 5608 df-f 5609 df-f1 5610 df-fo 5611 df-f1o 5612 df-fv 5613 df-riota 6282 df-ov 6323 df-oprab 6324 df-mpt2 6325 df-er 7394 df-en 7601 df-dom 7602 df-sdom 7603 df-pnf 9708 df-mnf 9709 df-xr 9710 df-ltxr 9711 df-le 9712 df-sub 9893 df-neg 9894 df-2 10701 df-3 10702 |
This theorem is referenced by: (None) |
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