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Mirrors > Home > ILE Home > Th. List > sbcfg | Unicode version |
Description: Distribute proper substitution through the function predicate with domain and codomain. (Contributed by Alexander van der Vekens, 15-Jul-2018.) |
Ref | Expression |
---|---|
sbcfg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-f 5186 | . . . 4 | |
2 | 1 | a1i 9 | . . 3 |
3 | 2 | sbcbidv 3004 | . 2 |
4 | sbcfng 5329 | . . . 4 | |
5 | sbcssg 3513 | . . . . 5 | |
6 | csbrng 5059 | . . . . . 6 | |
7 | 6 | sseq1d 3166 | . . . . 5 |
8 | 5, 7 | bitrd 187 | . . . 4 |
9 | 4, 8 | anbi12d 465 | . . 3 |
10 | sbcan 2988 | . . 3 | |
11 | df-f 5186 | . . 3 | |
12 | 9, 10, 11 | 3bitr4g 222 | . 2 |
13 | 3, 12 | bitrd 187 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wcel 2135 wsbc 2946 csb 3040 wss 3111 crn 4599 wfn 5177 wf 5178 |
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-v 2723 df-sbc 2947 df-csb 3041 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-br 3977 df-opab 4038 df-id 4265 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-rn 4609 df-fun 5184 df-fn 5185 df-f 5186 |
This theorem is referenced by: ctiunctlemf 12308 |
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