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Mirrors > Home > ILE Home > Th. List > funeqd | 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 5143 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1331 wfun 5117 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-in 3077 df-ss 3084 df-br 3930 df-opab 3990 df-rel 4546 df-cnv 4547 df-co 4548 df-fun 5125 |
This theorem is referenced by: funopg 5157 funsng 5169 funcnvuni 5192 f1eq1 5323 frecuzrdgtclt 10194 shftfn 10596 ennnfonelemfun 11930 ennnfonelemf1 11931 isstruct2im 11969 isstruct2r 11970 structfung 11976 setsfun 11994 setsfun0 11995 |
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