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Theorem axc10 2060
 Description: Show that the original axiom ax-c10 32167 can be derived from ax6 2059 and others. See ax6fromc10 32177 for the rederivation of ax6 2059 from ax-c10 32167. Normally, axc10 2060 should be used rather than ax-c10 32167, 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 2059 . . 3
2 con3 139 . . . 4
32al2imi 1683 . . 3
41, 3mtoi 181 . 2
5 axc7 1914 . 2
64, 5syl 17 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4  wal 1435 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-12 1907  ax-13 2055 This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1660 This theorem is referenced by: (None)
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