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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 1450). (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 2963 | . 2 | |
2 | sbcimdv.1 | . . . . 5 | |
3 | 2 | alrimiv 1867 | . . . 4 |
4 | spsbc 2966 | . . . 4 | |
5 | sbcim1 3003 | . . . 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 1346 wcel 2141 cvv 2730 wsbc 2955 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-sbc 2956 |
This theorem is referenced by: (None) |
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