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Theorem leqf 181
 Description: Equality theorem for lambda abstraction, using bound variable instead of distinct variables. (Contributed by Mario Carneiro, 8-Oct-2014.)
Hypotheses
Ref Expression
leqf.1
leqf.2
leqf.3
Assertion
Ref Expression
leqf
Distinct variable groups:   ,   ,   ,   ,,

Proof of Theorem leqf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 leqf.1 . . . . 5
21wl 66 . . . 4
3 wv 64 . . . 4
42, 3wc 50 . . 3
54wl 66 . 2
6 leqf.2 . . . . 5
76ax-cb1 29 . . . . . 6
81beta 92 . . . . . 6
97, 8a1i 28 . . . . 5
101, 6eqtypi 78 . . . . . . 7
1110beta 92 . . . . . 6
127, 11a1i 28 . . . . 5
131, 6, 9, 123eqtr4i 96 . . . 4
14 weq 41 . . . . 5
15 wv 64 . . . . 5
1610wl 66 . . . . . 6
1716, 3wc 50 . . . . 5
1814, 15ax-17 105 . . . . 5
191, 15ax-hbl1 103 . . . . . 6
203, 15ax-17 105 . . . . . 6
212, 3, 15, 19, 20hbc 110 . . . . 5
2210, 15ax-hbl1 103 . . . . . 6
2316, 3, 15, 22, 20hbc 110 . . . . 5
2414, 4, 15, 17, 18, 21, 23hbov 111 . . . 4
25 leqf.3 . . . 4
26 wv 64 . . . . . 6
272, 26wc 50 . . . . 5
2816, 26wc 50 . . . . 5
2926, 3weqi 76 . . . . . . 7
3029id 25 . . . . . 6
312, 26, 30ceq2 90 . . . . 5
3216, 26, 30ceq2 90 . . . . 5
3314, 27, 28, 31, 32oveq12 100 . . . 4
3429, 7eqid 83 . . . 4
3513, 24, 25, 33, 34ax-inst 113 . . 3
364, 35leq 91 . 2
372eta 178 . . 3
387, 37a1i 28 . 2
3916eta 178 . . 3
407, 39a1i 28 . 2
415, 36, 38, 403eqtr3i 97 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-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-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:  alrimi  182  axext  219  axrep  220
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