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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1fn 5330 | . . . 4 | |
2 | 1 | adantr 274 | . . 3 |
3 | simpr 109 | . . 3 | |
4 | df-f 5127 | . . 3 | |
5 | 2, 3, 4 | sylanbrc 413 | . 2 |
6 | df-f1 5128 | . . . 4 | |
7 | 6 | simprbi 273 | . . 3 |
8 | 7 | adantr 274 | . 2 |
9 | df-f1 5128 | . 2 | |
10 | 5, 8, 9 | sylanbrc 413 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wss 3071 ccnv 4538 crn 4540 wfun 5117 wfn 5118 wf 5119 wf1 5120 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-f 5127 df-f1 5128 |
This theorem is referenced by: f1ff1 5336 difinfsn 6985 |
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