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Mirrors > Home > ILE Home > Th. List > funeq | Unicode version |
Description: Equality theorem for function predicate. (Contributed by NM, 16-Aug-1994.) |
Ref | Expression |
---|---|
funeq |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqimss2 3224 |
. . 3
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2 | funss 5249 |
. . 3
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3 | 1, 2 | syl 14 |
. 2
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4 | eqimss 3223 |
. . 3
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5 | funss 5249 |
. . 3
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6 | 4, 5 | syl 14 |
. 2
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7 | 3, 6 | impbid 129 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2170 |
This theorem depends on definitions: df-bi 117 df-nf 1471 df-sb 1773 df-clab 2175 df-cleq 2181 df-clel 2184 df-nfc 2320 df-in 3149 df-ss 3156 df-br 4018 df-opab 4079 df-rel 4647 df-cnv 4648 df-co 4649 df-fun 5232 |
This theorem is referenced by: funeqi 5251 funeqd 5252 fununi 5298 funcnvuni 5299 cnvresid 5304 fneq1 5318 elpmg 6681 fundmeng 6824 |
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