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Theorem alrimiv 141
 Description: If one can prove where does not contain , then is true for all .
Hypothesis
Ref Expression
alrimiv.1
Assertion
Ref Expression
alrimiv
Distinct variable groups:   ,   ,

Proof of Theorem alrimiv
StepHypRef Expression
1 alrimiv.1 . . . 4
21ax-cb2 30 . . 3
3 wtru 40 . . . 4
41eqtru 76 . . . 4
53, 4eqcomi 70 . . 3
62, 5leq 81 . 2
71ax-cb1 29 . . 3
82wl 59 . . . 4
98alval 132 . . 3
107, 9a1i 28 . 2
116, 10mpbir 77 1
 Colors of variables: type var term Syntax hints:  hb 3  kc 5  kl 6   ke 7  kt 8  kbr 9   wffMMJ2 11  tal 112 This theorem is referenced by:  exlimdv2  156  ax4e  158  exlimd  171  axgen  197  ax10  200  ax11  201  axrep  207  axpow  208  axun  209 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-refl 39  ax-eqmp 42  ax-ded 43  ax-ceq 46  ax-beta 60  ax-distrc 61  ax-leq 62  ax-hbl1 93  ax-17 95  ax-inst 103 This theorem depends on definitions:  df-ov 65  df-al 116
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