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Theorem ax9lem3 28960
 Description: Lemma for ax9 1921. Similar to sp 1733, without using sp 1733, ax9 1921, or ax10 1916. (Contributed by NM, 7-Aug-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ax9lem3.a
ax9lem3.c
Assertion
Ref Expression
ax9lem3
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem ax9lem3
StepHypRef Expression
1 ax9lem3.a . 2
2 ax-17 1607 . . 3
3 ax9lem3.c . . . . . . . 8
43ax9lem1 28958 . . . . . . 7
5 ax-17 1607 . . . . . . 7
6 ax-11 1732 . . . . . . 7
74, 5, 6syl2im 34 . . . . . 6
8 con2 108 . . . . . . . 8
98al2imi 1552 . . . . . . 7
103, 9mtoi 169 . . . . . 6
117, 10syl6 29 . . . . 5
1211con4d 97 . . . 4
1312con3i 127 . . 3
142, 13alrimih 1556 . 2
151, 14mt3 171 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1531 This theorem is referenced by:  ax9lem4  28961  ax9lem7  28964  ax9lem8  28965  ax9lem9  28966  ax9lem12  28969  ax9lem13  28970  ax9lem15  28972  ax9lem17  28974  ax9vax9  28976 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-8 1666  ax-11 1732
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