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Mirrors > Home > ILE Home > Th. List > funcoeqres | Unicode version |
Description: Express a constraint on a composition as a constraint on the composand. (Contributed by Stefan O'Rear, 7-Mar-2015.) |
Ref | Expression |
---|---|
funcoeqres |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funcocnv2 5454 | . . . 4 | |
2 | 1 | coeq2d 4763 | . . 3 |
3 | coass 5119 | . . . 4 | |
4 | 3 | eqcomi 2168 | . . 3 |
5 | coires1 5118 | . . 3 | |
6 | 2, 4, 5 | 3eqtr3g 2220 | . 2 |
7 | coeq1 4758 | . 2 | |
8 | 6, 7 | sylan9req 2218 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1342 cid 4263 ccnv 4600 crn 4602 cres 4603 ccom 4605 wfun 5179 |
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 4097 ax-pow 4150 ax-pr 4184 |
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 2726 df-un 3118 df-in 3120 df-ss 3127 df-pw 3558 df-sn 3579 df-pr 3580 df-op 3582 df-br 3980 df-opab 4041 df-id 4268 df-xp 4607 df-rel 4608 df-cnv 4609 df-co 4610 df-dm 4611 df-rn 4612 df-res 4613 df-fun 5187 |
This theorem is referenced by: (None) |
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