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Mirrors > Home > ILE Home > Th. List > sbex | Unicode version |
Description: Move existential quantifier in and out of substitution. (Contributed by NM, 27-Sep-2003.) (Proof rewritten by Jim Kingdon, 12-Feb-2018.) |
Ref | Expression |
---|---|
sbex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbexyz 1956 | . . . 4 | |
2 | 1 | sbbii 1723 | . . 3 |
3 | sbexyz 1956 | . . 3 | |
4 | 2, 3 | bitri 183 | . 2 |
5 | ax-17 1491 | . . 3 | |
6 | 5 | sbco2v 1898 | . 2 |
7 | ax-17 1491 | . . . 4 | |
8 | 7 | sbco2v 1898 | . . 3 |
9 | 8 | exbii 1569 | . 2 |
10 | 4, 6, 9 | 3bitr3i 209 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wex 1453 wsb 1720 |
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-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 |
This theorem is referenced by: sbabel 2284 sbcex2 2934 sbcexg 2935 |
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