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Theorem ax9lem14 29222
 Description: Change bound variable without using sp 1748, ax9 1954, or ax10 1949. (Contributed by NM, 22-Jul-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ax9lem14.a
ax9lem14.b
ax9lem14.c
ax9lem14.d
ax9lem14.e
ax9lem14.f
Assertion
Ref Expression
ax9lem14
Distinct variable groups:   ,,,   ,,,

Proof of Theorem ax9lem14
StepHypRef Expression
1 ax9lem14.a . . 3
2 ax9lem14.b . . 3
3 ax9lem14.c . . 3
4 ax-17 1616 . . 3
5 ax-17 1616 . . 3
6 ax-8 1675 . . 3
71, 2, 3, 4, 5, 6ax9lem13 29221 . 2
8 ax9lem14.d . . 3
9 ax9lem14.e . . 3
10 ax9lem14.f . . 3
11 ax-17 1616 . . 3
12 ax-17 1616 . . 3
13 ax-8 1675 . . 3
148, 9, 10, 11, 12, 13ax9lem13 29221 . 2
157, 14syl 15 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1540 This theorem is referenced by:  ax9lem16  29224 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746
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