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Theorem exval 133

Description: Value of the 'there exists' predicate.

Hypothesis

Ref	Expression
alval.1

Assertion

Ref	Expression
exval

Distinct variable groups:   ,,   ,,

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Proof of Theorem exval Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		wex 129	. . 3
2		alval.1	. . 3
3	1, 2	wc 45	. 2
4		df-ex 121	. . 3
5	1, 2, 4	ceq1 79	. 2
6		wal 124	. . . 4
7		wim 127	. . . . . 6
8		wal 124	. . . . . . 7
9		wv 58	. . . . . . . . . 10
10		wv 58	. . . . . . . . . 10
11	9, 10	wc 45	. . . . . . . . 9
12		wv 58	. . . . . . . . 9
13	7, 11, 12	wov 64	. . . . . . . 8
14	13	wl 59	. . . . . . 7
15	8, 14	wc 45	. . . . . 6
16	7, 15, 12	wov 64	. . . . 5
17	16	wl 59	. . . 4
18	6, 17	wc 45	. . 3
19	9, 2	weqi 68	. . . . . . . . . . 11
20	19	id 25	. . . . . . . . . 10
21	9, 10, 20	ceq1 79	. . . . . . . . 9
22	7, 11, 12, 21	oveq1 89	. . . . . . . 8
23	13, 22	leq 81	. . . . . . 7
24	8, 14, 23	ceq2 80	. . . . . 6
25	7, 15, 12, 24	oveq1 89	. . . . 5
26	16, 25	leq 81	. . . 4
27	6, 17, 26	ceq2 80	. . 3
28	18, 2, 27	cl 106	. 2
29	3, 5, 28	eqtri 85	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   tim 111  tal 112  tex 113

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-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  df-an 118  df-im 119  df-ex 121

This theorem is referenced by:  exlimdv2  156  ax4e  158  exlimd  171

Copyright terms: Public domain

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