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Theorem ax5o 1765
 Description: Show that the original axiom ax-5o 2213 can be derived from ax-5 1566 and others. See ax5 2223 for the rederivation of ax-5 1566 from ax-5o 2213. 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
ax5o

Proof of Theorem ax5o
StepHypRef Expression
1 sp 1763 . . . 4
21con2i 114 . . 3
3 hbn1 1745 . . 3
4 hbn1 1745 . . . . 5
54con1i 123 . . . 4
65alimi 1568 . . 3
72, 3, 63syl 19 . 2
8 ax-5 1566 . 2
97, 8syl5 30 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1549 This theorem is referenced by:  ax4567  27578 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761 This theorem depends on definitions:  df-bi 178  df-ex 1551
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