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Theorem cbv 180
 Description: Change bound variables in a lambda abstraction. (Contributed by Mario Carneiro, 8-Oct-2014.)
Hypotheses
Ref Expression
cbv.1
cbv.2
Assertion
Ref Expression
cbv
Distinct variable groups:   ,   ,   ,,   ,

Proof of Theorem cbv
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 cbv.1 . 2
2 wv 64 . . 3
31, 2ax-17 105 . 2
4 cbv.2 . . . 4
51, 4eqtypi 78 . . 3
65, 2ax-17 105 . 2
71, 3, 6, 4cbvf 179 1
 Colors of variables: type var term Syntax hints:  tv 1  kl 6   ke 7  kt 8  kbr 9   wffMMJ2 11  wffMMJ2t 12 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 This theorem is referenced by:  ax10  213
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