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Mirrors > Home > ILE Home > Th. List > sbor | Unicode version |
Description: Logical OR inside and outside of substitution are equivalent. (Contributed by NM, 29-Sep-2002.) (Proof rewritten by Jim Kingdon, 3-Feb-2018.) |
Ref | Expression |
---|---|
sbor |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sborv 1862 | . . . 4 | |
2 | 1 | sbbii 1738 | . . 3 |
3 | sborv 1862 | . . 3 | |
4 | 2, 3 | bitri 183 | . 2 |
5 | ax-17 1506 | . . 3 | |
6 | 5 | sbco2vh 1918 | . 2 |
7 | ax-17 1506 | . . . 4 | |
8 | 7 | sbco2vh 1918 | . . 3 |
9 | ax-17 1506 | . . . 4 | |
10 | 9 | sbco2vh 1918 | . . 3 |
11 | 8, 10 | orbi12i 753 | . 2 |
12 | 4, 6, 11 | 3bitr3i 209 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wo 697 wsb 1735 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 |
This theorem is referenced by: sbcor 2953 sbcorg 2954 unab 3343 |
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