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Theorem alimdv 184
 Description: Deduction from Theorem 19.20 of [Margaris] p. 90. (Contributed by Mario Carneiro, 9-Oct-2014.)
Hypothesis
Ref Expression
alimdv.1
Assertion
Ref Expression
alimdv
Distinct variable groups:   ,   ,

Proof of Theorem alimdv
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 alimdv.1 . . . . . . 7
21ax-cb1 29 . . . . . 6
32wctr 34 . . . . 5
43ax4 150 . . . 4
52wctl 33 . . . 4
64, 5adantl 56 . . 3
76, 1syldan 36 . 2
8 wv 64 . . 3
9 wal 134 . . . 4
103wl 66 . . . 4
119, 10wc 50 . . 3
125, 8ax-17 105 . . 3
139, 8ax-17 105 . . . 4
143, 8ax-hbl1 103 . . . 4
159, 10, 8, 13, 14hbc 110 . . 3
165, 8, 11, 12, 15hbct 155 . 2
177, 16alrimi 182 1
 Colors of variables: type var term Syntax hints:  tv 1   ht 2  hb 3  kc 5  kl 6  kt 8  kct 10   wffMMJ2 11  tal 122 This theorem was proved from axioms:  ax-syl 15  ax-jca 17  ax-simpl 20  ax-simpr 21  ax-id 24  ax-trud 26  ax-cb1 29  ax-cb2 30  ax-wctl 31  ax-wctr 32  ax-weq 40  ax-refl 42  ax-eqmp 45  ax-ded 46  ax-wct 47  ax-wc 49  ax-ceq 51  ax-wv 63  ax-wl 65  ax-beta 67  ax-distrc 68  ax-leq 69  ax-distrl 70  ax-wov 71  ax-eqtypi 77  ax-eqtypri 80  ax-hbl1 103  ax-17 105  ax-inst 113  ax-eta 177 This theorem depends on definitions:  df-ov 73  df-al 126  df-an 128 This theorem is referenced by:  exnal1  187
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