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Mirrors > Home > MPE Home > Th. List > funeqd | Structured version Visualization version Unicode version |
Description: Equality deduction for the function predicate. (Contributed by NM, 23-Feb-2013.) |
Ref | Expression |
---|---|
funeqd.1 |
Ref | Expression |
---|---|
funeqd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funeqd.1 | . 2 | |
2 | funeq 5908 | . 2 | |
3 | 1, 2 | syl 17 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wceq 1483 wfun 5882 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-in 3581 df-ss 3588 df-br 4654 df-opab 4713 df-rel 5121 df-cnv 5122 df-co 5123 df-fun 5890 |
This theorem is referenced by: funopg 5922 funsng 5937 f1eq1 6096 f1ssf1 6168 fvn0ssdmfun 6350 funcnvuni 7119 fundmge2nop0 13274 funcnvs2 13658 funcnvs3 13659 funcnvs4 13660 shftfn 13813 isstruct2 15867 structfung 15872 setsfun 15893 setsfun0 15894 strle1 15973 monfval 16392 ismon 16393 monpropd 16397 isepi 16400 isfth 16574 estrres 16779 lubfun 16980 glbfun 16993 acsficl2d 17176 frlmphl 20120 eengbas 25861 ebtwntg 25862 ecgrtg 25863 elntg 25864 uhgrspansubgrlem 26182 istrl 26593 ispth 26619 isspth 26620 upgrwlkdvspth 26635 uhgrwkspthlem1 26649 uhgrwkspthlem2 26650 usgr2wlkspthlem1 26653 usgr2wlkspthlem2 26654 pthdlem1 26662 2spthd 26837 0spth 26987 3spthd 27036 trlsegvdeglem2 27081 trlsegvdeglem3 27082 ajfun 27716 fresf1o 29433 padct 29497 smatrcl 29862 esum2dlem 30154 omssubadd 30362 sitgf 30409 fperdvper 40133 ovnovollem1 40870 dfateq12d 41209 afvres 41252 fdivval 42333 |
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