Mathbox for Norm Megill < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ax9lem16 Unicode version

Theorem ax9lem16 29777
 Description: Lemma for ax9 1902. Similar to ax10 1897 but with distinct variables, without using sp 1728, ax9 1902, or ax10 1897. We used ax9lem6 29767 to eliminate 5 hypotheses that would otherwise be needed. (Contributed by NM, 7-Aug-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ax9lem16.b
ax9lem16.c
ax9lem16.f
ax9lem16.g
ax9lem16.i
ax9lem16.k
ax9lem16.l
ax9lem16.m
ax9lem16.n
ax9lem16.o
Assertion
Ref Expression
ax9lem16
Distinct variable group:   ,,,,

Proof of Theorem ax9lem16
StepHypRef Expression
1 ax9lem16.f . . 3
2 ax9lem16.k . . 3
3 ax9lem16.i . . 3
41, 2, 3ax9lem15 29776 . 2
5 ax9lem16.b . . . . 5
6 ax9lem16.n . . . . . 6
71, 3, 2, 6ax9lem6 29767 . . . . 5
8 ax9lem16.c . . . . . 6
91, 3, 7, 8ax9lem6 29767 . . . . 5
10 ax9lem16.l . . . . 5
11 ax9lem16.m . . . . 5
125, 7, 9, 8, 10, 11ax9lem14 29775 . . . 4
1310, 8, 5, 2ax9lem6 29767 . . . . . 6
146, 13, 5, 3ax9lem6 29767 . . . . 5
15 ax9lem16.o . . . . . 6
16 ax9lem16.g . . . . . 6
1715, 16, 1, 7ax9lem6 29767 . . . . 5
1814, 1, 17ax9lem15 29776 . . . 4
1912, 18syl 15 . . 3
2015, 16, 17, 6, 13, 8ax9lem14 29775 . . 3
2119, 20syl 15 . 2
224, 21syl 15 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1530 This theorem is referenced by:  ax9lem17  29778 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727 This theorem depends on definitions:  df-bi 177  df-ex 1532
 Copyright terms: Public domain W3C validator