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Mirrors > Home > ILE Home > Th. List > r19.32r | Unicode version |
Description: One direction of Theorem 19.32 of [Margaris] p. 90 with restricted quantifiers. For decidable propositions this is an equivalence. (Contributed by Jim Kingdon, 19-Aug-2018.) |
Ref | Expression |
---|---|
r19.32r.1 |
Ref | Expression |
---|---|
r19.32r |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r19.32r.1 | . . . 4 | |
2 | orc 633 | . . . . 5 | |
3 | 2 | a1d 22 | . . . 4 |
4 | 1, 3 | alrimi 1415 | . . 3 |
5 | df-ral 2311 | . . . 4 | |
6 | olc 632 | . . . . . 6 | |
7 | 6 | imim2i 12 | . . . . 5 |
8 | 7 | alimi 1344 | . . . 4 |
9 | 5, 8 | sylbi 114 | . . 3 |
10 | 4, 9 | jaoi 636 | . 2 |
11 | df-ral 2311 | . 2 | |
12 | 10, 11 | sylibr 137 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wo 629 wal 1241 wnf 1349 wcel 1393 wral 2306 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-gen 1338 ax-4 1400 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-ral 2311 |
This theorem is referenced by: r19.32vr 2458 |
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