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Theorem ax9lem18 29133
 Description: Lemma for ax9 1942. Similar to dveeq2 1968, 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
ax9lem18.a
ax9lem18.b
ax9lem18.e
ax9lem18.f
ax9lem18.i
ax9lem18.j
ax9lem18.k
ax9lem18.m
ax9lem18.p
ax9lem18.r
ax9lem18.t
ax9lem18.x
Assertion
Ref Expression
ax9lem18
Distinct variable groups:   ,,,,,   ,,,

Proof of Theorem ax9lem18
StepHypRef Expression
1 ax9lem18.a . 2
2 ax9lem18.b . 2
3 ax9lem18.e . 2
4 ax9lem18.f . 2
5 ax9lem18.i . 2
6 ax9lem18.j . 2
7 ax9lem18.k . 2
8 ax9lem18.m . 2
9 ax9lem18.p . 2
10 ax9lem18.r . 2
11 ax9lem18.t . 2
12 ax9lem18.x . . 3
1312, 6ax9lem2 29117 . 2
141, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13ax9lem17 29132 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1546 This theorem is referenced by:  ax9vax9  29134 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-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-nf 1551
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