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Theorem ax5o 1693
 Description: Show that the original axiom ax-5o 1694 can be derived from ax-5 1533 and others. See ax5 1695 for the rederivation of ax-5 1533 from ax-5o 1694. Part of the proof is based on the proof of Lemma 22 of [Monk2] p. 114. Normally, ax5o 1693 should be used rather than ax-5o 1694, except by theorems specifically studying the latter's properties. (Contributed by NM, 21-May-2008.) (Proof modification is discouraged.)
Assertion
Ref Expression
ax5o

Proof of Theorem ax5o
StepHypRef Expression
1 ax-4 1692 . . . 4
21con2i 114 . . 3
3 ax-6 1534 . . 3
4 ax-6 1534 . . . . . 6
54con1i 123 . . . . 5
65ax-gen 1536 . . . 4
7 ax-5 1533 . . . 4
86, 7ax-mp 10 . . 3
92, 3, 83syl 20 . 2
10 ax-5 1533 . 2
119, 10syl5 30 1
 Colors of variables: wff set class Syntax hints:   wn 5   wi 6  wal 1532 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-4 1692
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