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Theorem ax9lem6 29767
 Description: Lemma for ax9 1902. Helps reduce the number of hypotheses. (Contributed by NM, 7-Aug-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ax9lem6.a
ax9lem6.c
ax9lem6.d
ax9lem6.e
Assertion
Ref Expression
ax9lem6
Distinct variable group:   ,,,

Proof of Theorem ax9lem6
StepHypRef Expression
1 ax9lem6.e . 2
2 ax-17 1606 . . . 4
3 ax9lem6.a . . . . 5
4 ax9lem6.c . . . . 5
5 ax9lem6.d . . . . 5
6 ax-17 1606 . . . . 5
73ax9lem1 29762 . . . . . . 7
8 ax-8 1661 . . . . . . 7
97, 8syl 15 . . . . . 6
109con3d 125 . . . . 5
113, 4, 5, 6, 10ax9lem5 29766 . . . 4
122, 11alrimih 1555 . . 3
1312con3i 127 . 2
141, 13ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1530 This theorem is referenced by:  ax9lem16  29777  ax9lem17  29778  ax9vax9  29780 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-8 1661  ax-6 1715  ax-11 1727
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