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Mirrors > Home > MPE Home > Th. List > Mathboxes > predfrirr | Structured version Unicode version |
Description: Given a well-founded
relationship, ![]() |
Ref | Expression |
---|---|
predfrirr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frirr 4781 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | elpredg 27759 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 2 | anidms 645 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | 3 | notbid 294 |
. . . . 5
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5 | 1, 4 | syl5ibr 221 |
. . . 4
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6 | 5 | expd 436 |
. . 3
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7 | 6 | pm2.43b 50 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | predel 27764 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | 8 | con3i 135 |
. 2
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10 | 7, 9 | pm2.61d1 159 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1709 ax-7 1729 ax-9 1761 ax-10 1776 ax-11 1781 ax-12 1793 ax-13 1944 ax-ext 2429 ax-sep 4497 ax-nul 4505 ax-pr 4615 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1702 df-eu 2263 df-mo 2264 df-clab 2436 df-cleq 2442 df-clel 2445 df-nfc 2598 df-ne 2643 df-ral 2797 df-rex 2798 df-rab 2801 df-v 3056 df-sbc 3271 df-dif 3415 df-un 3417 df-in 3419 df-ss 3426 df-nul 3722 df-if 3876 df-sn 3962 df-pr 3964 df-op 3968 df-br 4377 df-opab 4435 df-fr 4763 df-xp 4930 df-cnv 4932 df-dm 4934 df-rn 4935 df-res 4936 df-ima 4937 df-pred 27745 |
This theorem is referenced by: wfrlem14 27857 |
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