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Mirrors > Home > ILE Home > Th. List > f1eq2 | Unicode version |
Description: Equality theorem for one-to-one functions. (Contributed by NM, 10-Feb-1997.) |
Ref | Expression |
---|---|
f1eq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | feq2 5305 | . . 3 | |
2 | 1 | anbi1d 461 | . 2 |
3 | df-f1 5177 | . 2 | |
4 | df-f1 5177 | . 2 | |
5 | 2, 3, 4 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1335 ccnv 4587 wfun 5166 wf 5168 wf1 5169 |
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 1427 ax-gen 1429 ax-4 1490 ax-17 1506 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-cleq 2150 df-fn 5175 df-f 5176 df-f1 5177 |
This theorem is referenced by: f1oeq2 5406 f1eq123d 5409 brdomg 6695 ennnfonelemen 12220 |
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