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Mirrors > Home > QLE Home > Th. List > u1lemab | 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 |
---|---|
u1lemab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-i1 44 | . . 3 | |
2 | 1 | ran 78 | . 2 |
3 | ax-a2 31 | . . . . 5 | |
4 | 3 | ran 78 | . . . 4 |
5 | coman2 186 | . . . . 5 | |
6 | coman1 185 | . . . . . 6 | |
7 | 6 | comcom2 183 | . . . . 5 |
8 | 5, 7 | fh2r 474 | . . . 4 |
9 | 4, 8 | ax-r2 36 | . . 3 |
10 | anass 76 | . . . . 5 | |
11 | anidm 111 | . . . . . 6 | |
12 | 11 | lan 77 | . . . . 5 |
13 | 10, 12 | ax-r2 36 | . . . 4 |
14 | 13 | ax-r5 38 | . . 3 |
15 | 9, 14 | ax-r2 36 | . 2 |
16 | 2, 15 | ax-r2 36 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wn 4 wo 6 wa 7 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: u1lemnonb 675 i1com 708 u1lem3 749 u1lem11 780 sadm3 838 negantlem2 849 negantlem3 850 negantlem10 861 neg3antlem1 864 oa4to4u 973 oa3-6lem 980 oa3-u1lem 985 oa3-u2lem 986 oa3-1to5 993 lem4.6.2e2 1081 |
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