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Mirrors > Home > ILE Home > Th. List > Mathboxes > fmelpw1o | Unicode version |
Description: With a formula one can associate an
element of , which
can therefore be thought of as the set of "truth values" (but
recall that
there are no other genuine truth values than and , by
nndc 846, which translate to and respectively by iftrue 3531
and iffalse 3534, giving pwtrufal 14030).
As proved in if0ab 13840, the associated element of is the extension, in , of the formula . (Contributed by BJ, 15-Aug-2024.) |
Ref | Expression |
---|---|
fmelpw1o |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1oex 6403 | . . 3 | |
2 | 0ex 4116 | . . 3 | |
3 | 1, 2 | ifelpwun 4468 | . 2 |
4 | un0 3448 | . . 3 | |
5 | 4 | pweqi 3570 | . 2 |
6 | 3, 5 | eleqtri 2245 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2141 cun 3119 c0 3414 cif 3526 cpw 3566 c1o 6388 |
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-in1 609 ax-in2 610 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-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-nul 4115 ax-pow 4160 ax-pr 4194 ax-un 4418 |
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-ral 2453 df-rex 2454 df-rab 2457 df-v 2732 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-nul 3415 df-if 3527 df-pw 3568 df-sn 3589 df-pr 3590 df-uni 3797 df-tr 4088 df-iord 4351 df-on 4353 df-suc 4356 df-1o 6395 |
This theorem is referenced by: bj-charfun 13842 |
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