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Mirrors > Home > ILE Home > Th. List > feq123d | 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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feq123d.3 |
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Ref | Expression |
---|---|
feq123d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | feq12d.1 |
. . 3
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2 | feq12d.2 |
. . 3
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3 | 1, 2 | feq12d 5385 |
. 2
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4 | feq123d.3 |
. . 3
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5 | feq3 5380 |
. . 3
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6 | 4, 5 | syl 14 |
. 2
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7 | 3, 6 | 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 2175 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-v 2762 df-un 3157 df-in 3159 df-ss 3166 df-sn 3624 df-pr 3625 df-op 3627 df-br 4030 df-opab 4091 df-rel 4662 df-cnv 4663 df-co 4664 df-dm 4665 df-rn 4666 df-fun 5248 df-fn 5249 df-f 5250 |
This theorem is referenced by: feq123 5387 feq23d 5391 csbwrdg 10933 |
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