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Mirrors > Home > ILE Home > Th. List > f1ocnvfvb | Unicode version |
Description: Relationship between the value of a one-to-one onto function and the value of its converse. (Contributed by NM, 20-May-2004.) |
Ref | Expression |
---|---|
f1ocnvfvb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1ocnvfv 5742 | . . 3 | |
2 | 1 | 3adant3 1006 | . 2 |
3 | fveq2 5481 | . . . . 5 | |
4 | 3 | eqcoms 2167 | . . . 4 |
5 | f1ocnvfv2 5741 | . . . . 5 | |
6 | 5 | eqeq2d 2176 | . . . 4 |
7 | 4, 6 | syl5ib 153 | . . 3 |
8 | 7 | 3adant2 1005 | . 2 |
9 | 2, 8 | impbid 128 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 967 wceq 1342 wcel 2135 ccnv 4598 wf1o 5182 cfv 5183 |
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-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4095 ax-pow 4148 ax-pr 4182 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2724 df-sbc 2948 df-un 3116 df-in 3118 df-ss 3125 df-pw 3556 df-sn 3577 df-pr 3578 df-op 3580 df-uni 3785 df-br 3978 df-opab 4039 df-id 4266 df-xp 4605 df-rel 4606 df-cnv 4607 df-co 4608 df-dm 4609 df-rn 4610 df-res 4611 df-ima 4612 df-iota 5148 df-fun 5185 df-fn 5186 df-f 5187 df-f1 5188 df-fo 5189 df-f1o 5190 df-fv 5191 |
This theorem is referenced by: f1ofveu 5825 f1ocnvfv3 5826 seq3f1olemstep 10427 1arith2 12287 ennnfonelem1 12303 txhmeo 12886 |
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