Step | Hyp | Ref
| Expression |
1 | | snmg 3709 |
. . 3
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2 | | fo1stresm 6156 |
. . 3
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3 | 1, 2 | syl 14 |
. 2
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4 | | moeq 2912 |
. . . . . 6
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5 | 4 | moani 2096 |
. . . . 5
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("
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6 | | vex 2740 |
. . . . . . . 8
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_V" |
7 | 6 | brres 4909 |
. . . . . . 7
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8 | | fo1st 6152 |
. . . . . . . . . . 11
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9 | | fofn 5436 |
. . . . . . . . . . 11
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:"     |
10 | 8, 9 | ax-mp 5 |
. . . . . . . . . 10
 |
11 | | vex 2740 |
. . . . . . . . . 10
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_V" |
12 | | fnbrfvb 5552 |
. . . . . . . . . 10
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13 | 10, 11, 12 | mp2an 426 |
. . . . . . . . 9
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14 | 13 | anbi1i 458 |
. . . . . . . 8
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15 | | elxp7 6165 |
. . . . . . . . . . 11
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16 | | eleq1 2240 |
. . . . . . . . . . . . . . 15
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("   
   |
17 | 16 | biimpa 296 |
. . . . . . . . . . . . . 14
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18 | 17 | adantrr 479 |
. . . . . . . . . . . . 13
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)"   |
19 | 18 | adantrl 478 |
. . . . . . . . . . . 12
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)"    |
20 | | elsni 3609 |
. . . . . . . . . . . . . 14
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21 | | eqopi 6167 |
. . . . . . . . . . . . . . 15
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("               |
22 | 21 | an12s 565 |
. . . . . . . . . . . . . 14
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23 | 20, 22 | sylanr2 405 |
. . . . . . . . . . . . 13
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)"      |
24 | 23 | adantrrl 486 |
. . . . . . . . . . . 12
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)" 
     |
25 | 19, 24 | jca 306 |
. . . . . . . . . . 11
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)" |
26 | 15, 25 | sylan2b 287 |
. . . . . . . . . 10
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27 | 26 | adantl 277 |
. . . . . . . . 9
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28 | | simprr 531 |
. . . . . . . . . . . 12
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29 | 28 | fveq2d 5515 |
. . . . . . . . . . 11
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30 | | simprl 529 |
. . . . . . . . . . . 12
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31 | | simpl 109 |
. . . . . . . . . . . 12
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  |
32 | | op1stg 6145 |
. . . . . . . . . . . 12
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33 | 30, 31, 32 | syl2anc 411 |
. . . . . . . . . . 11
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<."      |
34 | 29, 33 | eqtrd 2210 |
. . . . . . . . . 10
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    
      |
35 | | snidg 3620 |
. . . . . . . . . . . . 13
     |
36 | 35 | adantr 276 |
. . . . . . . . . . . 12
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    
    |
37 | | opelxpi 4655 |
. . . . . . . . . . . 12
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     
      |
38 | 30, 36, 37 | syl2anc 411 |
. . . . . . . . . . 11
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    
  
      |
39 | 28, 38 | eqeltrd 2254 |
. . . . . . . . . 10
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    

     |
40 | 34, 39 | jca 306 |
. . . . . . . . 9
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41 | 27, 40 | impbida 596 |
. . . . . . . 8
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42 | 14, 41 | bitr3id 194 |
. . . . . . 7
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43 | 7, 42 | bitrid 192 |
. . . . . 6
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44 | 43 | mobidv 2062 |
. . . . 5
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45 | 5, 44 | mpbiri 168 |
. . . 4
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)"    |
46 | 45 | alrimiv 1874 |
. . 3
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47 | | funcnv2 5272 |
. . 3
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)"
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48 | 46, 47 | sylibr 134 |
. 2
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49 | | dff1o3 5463 |
. 2
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50 | 3, 48, 49 | sylanbrc 417 |
1
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