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Mirrors > Home > ILE Home > Th. List > f1ssr | Unicode version |
Description: Combine a one-to-one function with a restriction on the domain. (Contributed by Stefan O'Rear, 20-Feb-2015.) |
Ref | Expression |
---|---|
f1ssr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1fn 5419 |
. . . 4
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2 | 1 | adantr 276 |
. . 3
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3 | simpr 110 |
. . 3
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4 | df-f 5216 |
. . 3
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5 | 2, 3, 4 | sylanbrc 417 |
. 2
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6 | df-f1 5217 |
. . . 4
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7 | 6 | simprbi 275 |
. . 3
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8 | 7 | adantr 276 |
. 2
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9 | df-f1 5217 |
. 2
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10 | 5, 8, 9 | sylanbrc 417 |
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 |
This theorem depends on definitions: df-bi 117 df-f 5216 df-f1 5217 |
This theorem is referenced by: f1ff1 5425 difinfsn 7093 |
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