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Mirrors > Home > QLE Home > Th. List > u1lemaa | Unicode version |
Description: Lemma for Sasaki implication study. Equation 4.10 of [MegPav2000] p. 23. This is the second part of the equation. |
Ref | Expression |
---|---|
u1lemaa |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-i1 44 | . . 3 | |
2 | 1 | ran 78 | . 2 |
3 | comid 187 | . . . . 5 | |
4 | 3 | comcom2 183 | . . . 4 |
5 | comanr1 464 | . . . 4 | |
6 | 4, 5 | fh1r 473 | . . 3 |
7 | ax-a2 31 | . . . . 5 | |
8 | an32 83 | . . . . . . 7 | |
9 | anidm 111 | . . . . . . . 8 | |
10 | 9 | ran 78 | . . . . . . 7 |
11 | 8, 10 | ax-r2 36 | . . . . . 6 |
12 | ancom 74 | . . . . . . 7 | |
13 | dff 101 | . . . . . . . 8 | |
14 | 13 | ax-r1 35 | . . . . . . 7 |
15 | 12, 14 | ax-r2 36 | . . . . . 6 |
16 | 11, 15 | 2or 72 | . . . . 5 |
17 | 7, 16 | ax-r2 36 | . . . 4 |
18 | or0 102 | . . . 4 | |
19 | 17, 18 | ax-r2 36 | . . 3 |
20 | 6, 19 | ax-r2 36 | . 2 |
21 | 2, 20 | ax-r2 36 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wn 4 wo 6 wa 7 wf 9 wi1 12 |
This theorem was proved from axioms: ax-a1 30 ax-a2 31 ax-a3 32 ax-a4 33 ax-a5 34 ax-r1 35 ax-r2 36 ax-r4 37 ax-r5 38 ax-r3 439 |
This theorem depends on definitions: df-b 39 df-a 40 df-t 41 df-f 42 df-i1 44 df-le1 130 df-le2 131 df-c1 132 df-c2 133 |
This theorem is referenced by: u1lemnona 665 u12lembi 726 u1lem5 761 negantlem2 849 kb10iii 893 oas 925 oau 929 oaur 930 oa6to4 958 oa8to5 972 |
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