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Theorem axc4 1938
 Description: Show that the original axiom ax-c4 32456 can be derived from ax-4 1682 and others. See ax4 32466 for the rederivation of ax-4 1682 from ax-c4 32456. Part of the proof is based on the proof of Lemma 22 of [Monk2] p. 114. (Contributed by NM, 21-May-2008.) (Proof modification is discouraged.)
Assertion
Ref Expression
axc4

Proof of Theorem axc4
StepHypRef Expression
1 sp 1937 . . . 4
21con2i 124 . . 3
3 hbn1 1916 . . 3
4 hbn1 1916 . . . . 5
54con1i 133 . . . 4
65alimi 1684 . . 3
72, 3, 63syl 18 . 2
8 alim 1683 . 2
97, 8syl5 33 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4  wal 1442 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-12 1933 This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1664 This theorem is referenced by:  axc5c4c711  36752
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