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Theorem axc11-o 2281
Description: Show that ax-c11 2218 can be derived from ax-c11n 2219. An open problem is whether this theorem can be derived from ax-c11n 2219 and the others when ax-12 1854 is replaced with ax-c15 2220. See theorem axc11nfromc11 2256 for the rederivation of ax-c11n 2219 from axc11 2054.

Normally, axc11 2054 should be used rather than ax-c11 2218 or axc11-o 2281, except by theorems specifically studying the latter's properties. (Contributed by NM, 16-May-2008.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion
Ref Expression
axc11-o

Proof of Theorem axc11-o
StepHypRef Expression
1 ax-c11n 2219 . 2
2 ax12 2234 . . . 4
32equcoms 1795 . . 3
43sps-o 2238 . 2
5 pm2.27 39 . . 3
65al2imi 1636 . 2
71, 4, 6sylsyld 56 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  A.wal 1393
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-11 1842  ax-c5 2214  ax-c4 2215  ax-c7 2216  ax-c11 2218  ax-c11n 2219  ax-c15 2220  ax-c9 2221
This theorem depends on definitions:  df-bi 185  df-ex 1613
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