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Mirrors > Home > MPE Home > Th. List > f1eq3 | Structured version Visualization version Unicode version |
Description: Equality theorem for one-to-one functions. (Contributed by NM, 10-Feb-1997.) |
Ref | Expression |
---|---|
f1eq3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | feq3 5694 |
. . 3
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2 | 1 | anbi1d 716 |
. 2
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3 | df-f1 5566 |
. 2
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4 | df-f1 5566 |
. 2
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5 | 2, 3, 4 | 3bitr4g 296 |
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 1673 ax-4 1686 ax-5 1762 ax-6 1809 ax-7 1855 ax-10 1919 ax-11 1924 ax-12 1937 ax-13 2092 ax-ext 2432 |
This theorem depends on definitions: df-bi 190 df-an 377 df-tru 1451 df-ex 1668 df-nf 1672 df-sb 1802 df-clab 2439 df-cleq 2445 df-clel 2448 df-in 3379 df-ss 3386 df-f 5565 df-f1 5566 |
This theorem is referenced by: f1oeq3 5790 f1eq123d 5792 tposf12 6985 brdomg 7566 pwfseq 9076 f1linds 19394 isuslgra 25082 isusgra 25083 isusgra0 25086 usgraop 25089 cusgraexilem2 25207 diaf1oN 34700 isusgrs 39343 usgr1vr 39431 usgrexi 39608 |
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