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Theorem exnal1 175

Description: Forward direction of exnal 188.

Hypothesis

Ref	Expression
alnex1.1

Assertion

Ref	Expression
exnal1

Distinct variable group:   ,

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Proof of Theorem exnal1

Step	Hyp	Ref	Expression
1		wex 129	. . . 4
2		wnot 128	. . . . . 6
3		alnex1.1	. . . . . 6
4	2, 3	wc 45	. . . . 5
5	4	wl 59	. . . 4
6	1, 5	wc 45	. . 3
7	3	notnot1 150	. . . . . 6
8		wtru 40	. . . . . 6
9	7, 8	adantl 51	. . . . 5
10	9	alimdv 172	. . . 4
11		wal 124	. . . . . . 7
12	2, 4	wc 45	. . . . . . . 8
13	12	wl 59	. . . . . . 7
14	11, 13	wc 45	. . . . . 6
15	14	id 25	. . . . 5
16	4	alnex 174	. . . . . 6
17	14, 16	a1i 28	. . . . 5
18	15, 17	mpbi 72	. . . 4
19	10, 18	syl 16	. . 3
20	6, 19	con2d 151	. 2
21	20	trul 37	1

Colors of variables: type var term

Syntax hints:   ht 2  hb 3  kc 5  kl 6   ke 7  kt 8  kbr 9  kct 10   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

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

This theorem is referenced by: (None)

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