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Theorem ax9lem13 29128
 Description: Lemma for ax9 1942. Similar to cbv3 2008 with distinct variables, without using sp 1755, ax9 1942, or ax10 1976. (Contributed by NM, 7-Aug-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ax9lem13.a
ax9lem13.c
ax9lem13.d
ax9lem13.1
ax9lem13.2
ax9lem13.3
Assertion
Ref Expression
ax9lem13
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem ax9lem13
StepHypRef Expression
1 ax9lem13.1 . . 3
21alimi 1565 . 2
3 ax9lem13.d . . . . 5
4 ax9lem13.a . . . . . . 7
5 ax9lem13.c . . . . . . 7
6 id 20 . . . . . . . 8
76hbth 1558 . . . . . . . . 9
84, 5ax9lem7 29122 . . . . . . . . . 10
98a1i 11 . . . . . . . . 9
10 ax9lem13.2 . . . . . . . . . 10
1110a1i 11 . . . . . . . . 9
124, 5, 7, 9, 11ax9lem9 29124 . . . . . . . 8
136, 12ax-mp 8 . . . . . . 7
144, 5, 13ax9lem8 29123 . . . . . 6
154, 5ax9lem3 29118 . . . . . . . 8
16 ax9lem13.3 . . . . . . . 8
1715, 16syl5 30 . . . . . . 7
1817con3i 129 . . . . . 6
1914, 18alrimih 1571 . . . . 5
203, 19mt3 173 . . . 4
2120alimi 1565 . . 3
2221a7s 1742 . 2
232, 22syl 16 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1546 This theorem is referenced by:  ax9lem14  29129 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-8 1682  ax-6 1736  ax-7 1741  ax-11 1753
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