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Theorem clf 115
 Description: Evaluate a lambda expression. (Contributed by Mario Carneiro, 8-Oct-2014.)
Hypotheses
Ref Expression
clf.1
clf.2
clf.3
clf.4
clf.5
Assertion
Ref Expression
clf
Distinct variable groups:   ,   ,   ,   ,,

Proof of Theorem clf
StepHypRef Expression
1 clf.2 . 2
2 clf.1 . . . . 5
32wl 66 . . . 4
43, 1wc 50 . . 3
5 clf.3 . . . 4
62, 5eqtypi 78 . . 3
74, 6weqi 76 . 2
8 clf.4 . . . 4
98ax-cb1 29 . . 3
102beta 92 . . 3
119, 10a1i 28 . 2
12 weq 41 . . 3
13 wv 64 . . 3
1412, 13, 9a17i 106 . . 3
152, 13, 9hbl1 104 . . . 4
16 clf.5 . . . 4
173, 1, 13, 15, 16hbc 110 . . 3
1812, 4, 13, 6, 14, 17, 8hbov 111 . 2
19 wv 64 . . . 4
203, 19wc 50 . . 3
2119, 1weqi 76 . . . . 5
2221id 25 . . . 4
233, 19, 22ceq2 90 . . 3
2412, 20, 2, 23, 5oveq12 100 . 2
251, 7, 11, 18, 24insti 114 1
 Colors of variables: type var term Syntax hints:  tv 1   ht 2  hb 3  kc 5  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-wc 49  ax-ceq 51  ax-wv 63  ax-wl 65  ax-beta 67  ax-distrc 68  ax-leq 69  ax-wov 71  ax-eqtypi 77  ax-eqtypri 80  ax-hbl1 103  ax-17 105  ax-inst 113 This theorem depends on definitions:  df-ov 73 This theorem is referenced by:  cl  116  cbvf  179  exmid  199  axrep  220
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