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Theorem exnal 188

Description: Theorem 19.14 of [Margaris] p. 90.

Hypothesis

Ref	Expression
exmid.1

Assertion

Ref	Expression
exnal

Distinct variable groups:   ,   ,

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Proof of Theorem exnal

Step	Hyp	Ref	Expression
1		wnot 128	. . 3
2		wex 129	. . . . 5
3		exmid.1	. . . . . . 7
4	1, 3	wc 45	. . . . . 6
5	4	wl 59	. . . . 5
6	2, 5	wc 45	. . . 4
7	1, 6	wc 45	. . 3
8	1, 7	wc 45	. 2
9		wal 124	. . . . 5
10	1, 4	wc 45	. . . . . 6
11	10	wl 59	. . . . 5
12	9, 11	wc 45	. . . 4
13	4	alnex 174	. . . 4
14	12, 13	eqcomi 70	. . 3
15	1, 7, 14	ceq2 80	. 2
16	6	notnot 187	. 2
17	3	wl 59	. . . 4
18	9, 17	wc 45	. . 3
19	3	notnot 187	. . . . 5
20	3, 19	leq 81	. . . 4
21	9, 17, 20	ceq2 80	. . 3
22	1, 18, 21	ceq2 80	. 2
23	8, 15, 16, 22	3eqtr4i 86	1

Colors of variables: type var term

Syntax hints:   ht 2  hb 3  kc 5  kl 6   ke 7  kt 8  kbr 9   wffMMJ2 11  wffMMJ2t 12   tne 110  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-ded 43  ax-ceq 46  ax-beta 60  ax-distrc 61  ax-leq 62  ax-distrl 63  ax-hbl1 93  ax-17 95  ax-inst 103  ax-eta 165  ax-ac 183

This theorem depends on definitions:  df-ov 65  df-al 116  df-fal 117  df-an 118  df-im 119  df-not 120  df-ex 121  df-or 122

This theorem is referenced by: (None)

Copyright terms: Public domain

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