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Mirrors > Home > MPE Home > Th. List > fores | Structured version Visualization version Unicode version |
Description: Restriction of an onto function. (Contributed by NM, 4-Mar-1997.) |
Ref | Expression |
---|---|
fores |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funres 5640 |
. . 3
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2 | 1 | anim1i 576 |
. 2
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3 | df-fn 5604 |
. . 3
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4 | df-ima 4866 |
. . . . 5
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5 | 4 | eqcomi 2471 |
. . . 4
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6 | df-fo 5607 |
. . . 4
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7 | 5, 6 | mpbiran2 935 |
. . 3
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8 | ssdmres 5145 |
. . . 4
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9 | 8 | anbi2i 705 |
. . 3
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10 | 3, 7, 9 | 3bitr4i 285 |
. 2
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11 | 2, 10 | sylibr 217 |
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-9 1907 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 ax-sep 4539 ax-nul 4548 ax-pr 4653 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-ral 2754 df-rex 2755 df-rab 2758 df-v 3059 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-nul 3744 df-if 3894 df-sn 3981 df-pr 3983 df-op 3987 df-br 4417 df-opab 4476 df-xp 4859 df-rel 4860 df-cnv 4861 df-co 4862 df-dm 4863 df-res 4865 df-ima 4866 df-fun 5603 df-fn 5604 df-fo 5607 |
This theorem is referenced by: resdif 5857 f1oweALT 6804 imafi 7893 f1opwfi 7904 fodomfi2 8517 fin1a2lem7 8862 znnen 14314 conima 20489 1stcfb 20509 1stckgenlem 20617 qtoprest 20781 re2ndc 21868 uniiccdif 22584 opnmblALT 22610 mbfimaopnlem 22660 ghsubgolemOLD 26147 ffsrn 28363 erdszelem2 29964 ivthALT 31040 poimirlem26 32011 poimirlem27 32012 lmhmfgima 35987 |
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