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Theorem ax5o 1749
Description: Show that the original axiom ax-5o 2136 can be derived from ax-5 1557 and others. See ax5 2146 for the rederivation of ax-5 1557 from ax-5o 2136.

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 1747 . . . 4
21con2i 112 . . 3
3 hbn1 1730 . . 3
4 hbn1 1730 . . . . 5
54con1i 121 . . . 4
65alimi 1559 . . 3
72, 3, 63syl 18 . 2
8 ax-5 1557 . 2
97, 8syl5 28 1
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4  wal 1540
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-ex 1542
This theorem is referenced by: (None)
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