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Mirrors > Home > MPE Home > Th. List > isoeq4 | Structured version Unicode version |
Description: Equality theorem for isomorphisms. (Contributed by NM, 17-May-2004.) |
Ref | Expression |
---|---|
isoeq4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1oeq2 5731 |
. . 3
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2 | raleq 3013 |
. . . 4
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3 | 2 | raleqbi1dv 3021 |
. . 3
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4 | 1, 3 | anbi12d 710 |
. 2
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5 | df-isom 5525 |
. 2
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6 | df-isom 5525 |
. 2
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7 | 4, 5, 6 | 3bitr4g 288 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-ext 2430 |
This theorem depends on definitions: df-bi 185 df-an 371 df-tru 1373 df-ex 1588 df-nf 1591 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ral 2800 df-fn 5519 df-f 5520 df-f1 5521 df-fo 5522 df-f1o 5523 df-isom 5525 |
This theorem is referenced by: oieu 7854 oiid 7856 finnisoeu 8384 iunfictbso 8385 fz1isolem 12316 isercolllem3 13246 summolem2a 13294 erdszelem1 27213 erdsze 27224 erdsze2lem1 27225 erdsze2lem2 27226 prodmolem2a 27581 |
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