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Theorem ax9lem11 29221
 Description: Lemma for ax9 1962. Similar to exlimih 1810, without using sp 1753, ax9 1962, or ax10 1957. (Contributed by NM, 7-Aug-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ax9lem11.a
ax9lem11.c
ax9lem11.1
ax9lem11.2
Assertion
Ref Expression
ax9lem11
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem ax9lem11
StepHypRef Expression
1 ax9lem11.2 . . 3
21eximi 1581 . 2
3 df-ex 1547 . . 3
4 ax9lem11.a . . . . 5
5 ax9lem11.c . . . . 5
6 ax9lem11.1 . . . . 5
74, 5, 6ax9lem8 29218 . . . 4
87con1i 121 . . 3
93, 8sylbi 187 . 2
102, 9syl 15 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1545  wex 1546 This theorem is referenced by:  ax9lem15  29225 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1551  ax-5 1562  ax-17 1621  ax-8 1680  ax-6 1734  ax-11 1751 This theorem depends on definitions:  df-bi 177  df-ex 1547
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