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Mirrors > Home > ILE Home > Th. List > feqmptd | Unicode version |
Description: Deduction form of dffn5im 5526. (Contributed by Mario Carneiro, 8-Jan-2015.) |
Ref | Expression |
---|---|
feqmptd.1 |
Ref | Expression |
---|---|
feqmptd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | feqmptd.1 | . . 3 | |
2 | ffn 5331 | . . 3 | |
3 | 1, 2 | syl 14 | . 2 |
4 | dffn5im 5526 | . 2 | |
5 | 3, 4 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1342 cmpt 4037 wfn 5177 wf 5178 cfv 5182 |
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 4094 ax-pow 4147 ax-pr 4181 |
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 2723 df-sbc 2947 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-opab 4038 df-mpt 4039 df-id 4265 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-iota 5147 df-fun 5184 df-fn 5185 df-f 5186 df-fv 5190 |
This theorem is referenced by: feqresmpt 5534 cofmpt 5648 fcoconst 5650 suppssof1 6061 ofco 6062 caofinvl 6066 caofcom 6067 mapxpen 6805 xpmapenlem 6806 cnrecnv 10838 lmcn2 12827 cnmpt11f 12831 cnmpt21f 12839 cncfmpt1f 13131 negfcncf 13136 cnrehmeocntop 13140 dvcnp2cntop 13210 dvimulf 13217 dvcoapbr 13218 dvcj 13220 dvfre 13221 dvmptcjx 13233 dvef 13235 |
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