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Theorem ax5o 1761
 Description: Show that the original axiom ax-5o 2184 can be derived from ax-5 1563 and others. See ax5 2194 for the rederivation of ax-5 1563 from ax-5o 2184. 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 1759 . . . 4
21con2i 114 . . 3
3 hbn1 1741 . . 3
4 hbn1 1741 . . . . 5
54con1i 123 . . . 4
65alimi 1565 . . 3
72, 3, 63syl 19 . 2
8 ax-5 1563 . 2
97, 8syl5 30 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1546 This theorem is referenced by:  ax4567  27286 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-11 1757 This theorem depends on definitions:  df-bi 178  df-ex 1548
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