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Mirrors > Home > ILE Home > Th. List > foeq3 | Unicode version |
Description: Equality theorem for onto functions. (Contributed by NM, 1-Aug-1994.) |
Ref | Expression |
---|---|
foeq3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq2 2127 | . . 3 | |
2 | 1 | anbi2d 459 | . 2 |
3 | df-fo 5099 | . 2 | |
4 | df-fo 5099 | . 2 | |
5 | 2, 3, 4 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1316 crn 4510 wfn 5088 wfo 5091 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1408 ax-gen 1410 ax-4 1472 ax-17 1491 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-cleq 2110 df-fo 5099 |
This theorem is referenced by: f1oeq3 5328 foeq123d 5331 resdif 5357 ffoss 5367 fifo 6836 enumct 6968 ctssexmid 6992 exmidfodomrlemr 7026 exmidfodomrlemrALT 7027 qnnen 11871 unct 11881 subctctexmid 13123 |
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