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Theorem axc10 2004
Description: Show that the original axiom ax-c10 2217 can be derived from ax6 2003 and others. See ax6fromc10 2227 for the rederivation of ax6 2003 from ax-c10 2217.

Normally, axc10 2004 should be used rather than ax-c10 2217, except by theorems specifically studying the latter's properties. (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.)

Assertion
Ref Expression
axc10

Proof of Theorem axc10
StepHypRef Expression
1 ax6 2003 . . 3
2 con3 134 . . . 4
32al2imi 1636 . . 3
41, 3mtoi 178 . 2
5 axc7 1861 . 2
64, 5syl 16 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->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-10 1837  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613
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