Description: Show that [_ R / s ]_ N is under P .\/ Q when R .<_ ( P .\/ Q ) . (Contributed by NM, 19-Mar-2013)
Ref | Expression | ||
---|---|---|---|
Hypotheses | cdleme32.b | |
|
cdleme32.l | |
||
cdleme32.j | |
||
cdleme32.m | |
||
cdleme32.a | |
||
cdleme32.h | |
||
cdleme32.u | |
||
cdleme32.c | |
||
cdleme32.d | |
||
cdleme32.e | |
||
cdleme32.i | |
||
cdleme32.n | |
||
cdleme32a1.y | |
||
cdleme32a1.z | |
||
Assertion | cdleme41sn3a | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdleme32.b | |
|
2 | cdleme32.l | |
|
3 | cdleme32.j | |
|
4 | cdleme32.m | |
|
5 | cdleme32.a | |
|
6 | cdleme32.h | |
|
7 | cdleme32.u | |
|
8 | cdleme32.c | |
|
9 | cdleme32.d | |
|
10 | cdleme32.e | |
|
11 | cdleme32.i | |
|
12 | cdleme32.n | |
|
13 | cdleme32a1.y | |
|
14 | cdleme32a1.z | |
|
15 | simp2rl | |
|
16 | simp3 | |
|
17 | 10 11 12 13 14 | cdleme31sn1c | |
18 | 15 16 17 | syl2anc | |
19 | 1 | fvexi | |
20 | nfv | |
|
21 | nfra1 | |
|
22 | nfcv | |
|
23 | 21 22 | nfriota | |
24 | 14 23 | nfcxfr | |
25 | nfcv | |
|
26 | nfcv | |
|
27 | 24 25 26 | nfbr | |
28 | 27 | a1i | |
29 | 14 | a1i | |
30 | breq1 | |
|
31 | 30 | adantl | |
32 | simpl11 | |
|
33 | simp12l | |
|
34 | 33 | adantr | |
35 | simp13l | |
|
36 | 35 | adantr | |
37 | 15 | adantr | |
38 | simprl | |
|
39 | 2 3 4 5 6 7 9 13 | cdleme4a | |
40 | 32 34 36 37 38 39 | syl131anc | |
41 | 40 | ex | |
42 | simp1 | |
|
43 | simp2rr | |
|
44 | simp2l | |
|
45 | 1 2 3 4 5 6 7 9 13 14 | cdleme25cl | |
46 | 42 15 43 44 16 45 | syl122anc | |
47 | simp11 | |
|
48 | simp12 | |
|
49 | simp13 | |
|
50 | 2 3 5 6 | cdlemb2 | |
51 | 47 48 49 44 50 | syl121anc | |
52 | 20 28 29 31 41 46 51 | riotasv3d | |
53 | 19 52 | mpan2 | |
54 | 18 53 | eqbrtrd | |