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| Description: Re-derivation of ax-6o 1019 from ax467 1064. Note that ax-6o 1019 and ax-7 1003 are not used by the re-derivation. The use of 19.20i 1033 (which uses ax-4 1014) is allowed since we have already proved ax467to4 1065. |
| Ref | Expression |
|---|---|
| ax467to6 |
     
  |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax467to4 1065 |
. . . 4
| |
| 2 | hba1 1044 |
. . . . . 6
| |
| 3 | 2 | con3i 104 |
. . . . 5
|
| 4 | 3 | 19.20i 1033 |
. . . 4
|
| 5 | 1, 4 | syl 10 |
. . 3
|
| 6 | 5 | con3i 104 |
. 2
|
| 7 | pm2.21 79 |
. 2
| |
| 8 | ax467 1064 |
. 2
| |
| 9 | 6, 7, 8 | 3syl 20 |
1
|
| Colors of variables: wff set class |
| Syntax hints: wn 2
wi 3
wal 995 |
| This theorem is referenced by: ax467to7 1067 |
| This theorem was proved from axioms: ax-1 4 ax-2 5 ax-3 6 ax-mp 7 ax-7 1003 ax-gen 1004 ax-4 1014 ax-5o 1016 ax-6o 1019 |