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Mirrors > Home > ILE Home > Th. List > feq12d | Unicode version |
Description: Equality deduction for functions. (Contributed by Paul Chapman, 22-Jun-2011.) |
Ref | Expression |
---|---|
feq12d.1 |
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feq12d.2 |
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Ref | Expression |
---|---|
feq12d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | feq12d.1 |
. . 3
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2 | 1 | feq1d 5371 |
. 2
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3 | feq12d.2 |
. . 3
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4 | 3 | feq2d 5372 |
. 2
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5 | 2, 4 | bitrd 188 |
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 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-sn 3613 df-pr 3614 df-op 3616 df-br 4019 df-opab 4080 df-rel 4651 df-cnv 4652 df-co 4653 df-dm 4654 df-rn 4655 df-fun 5237 df-fn 5238 df-f 5239 |
This theorem is referenced by: feq123d 5375 smoeq 6316 lmbr2 14191 lmff 14226 limccl 14605 ellimc3apf 14606 bj-charfundcALT 15039 |
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