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Mirrors > Home > ILE Home > Th. List > sbcimdv | Unicode version |
Description: Substitution analogue of Theorem 19.20 of [Margaris] p. 90 (alim 1418). (Contributed by NM, 11-Nov-2005.) (Revised by NM, 17-Aug-2018.) (Proof shortened by JJ, 7-Jul-2021.) |
Ref | Expression |
---|---|
sbcimdv.1 |
Ref | Expression |
---|---|
sbcimdv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcex 2890 | . 2 | |
2 | sbcimdv.1 | . . . . 5 | |
3 | 2 | alrimiv 1830 | . . . 4 |
4 | spsbc 2893 | . . . 4 | |
5 | sbcim1 2929 | . . . 4 | |
6 | 3, 4, 5 | syl56 34 | . . 3 |
7 | 6 | com3l 81 | . 2 |
8 | 1, 7 | mpdi 43 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1314 wcel 1465 cvv 2660 wsbc 2882 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-sbc 2883 |
This theorem is referenced by: (None) |
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