Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax16g-o Unicode version

Theorem ax16g-o 2264
 Description: A generalization of axiom ax-c16 2223. Version of axc16g 1940 using ax-c11 2218. (Contributed by NM, 15-May-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax16g-o
Distinct variable group:   ,

Proof of Theorem ax16g-o
StepHypRef Expression
1 aev-o 2261 . 2
2 ax-c16 2223 . 2
3 biidd 237 . . . 4
43dral1-o 2233 . . 3
54biimprd 223 . 2
61, 2, 5sylsyld 56 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  A.wal 1393 This theorem is referenced by:  ax12inda2  2277 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-c5 2214  ax-c4 2215  ax-c7 2216  ax-c11 2218  ax-c9 2221  ax-c16 2223 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
 Copyright terms: Public domain W3C validator