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Theorem ax4g 139

Description: If is true for all , then it is true for .

Hypotheses

Ref	Expression
ax4g.1
ax4g.2

Assertion

Ref	Expression
ax4g

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Proof of Theorem ax4g Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		wal 124	. . . 4
2		ax4g.1	. . . 4
3	1, 2	wc 45	. . 3
4	3	trud 27	. 2
5		ax4g.2	. . . 4
6	2, 5	wc 45	. . 3
7	4	ax-cb1 29	. . . . . 6
8	7	id 25	. . . . 5
9	2	alval 132	. . . . . 6
10	7, 9	a1i 28	. . . . 5
11	8, 10	mpbi 72	. . . 4
12	2, 5, 11	ceq1 79	. . 3
13	5, 4	hbth 99	. . 3
14	6, 12, 13	eqtri 85	. 2
15	4, 14	mpbir 77	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  tal 112

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-hbl1 93  ax-17 95  ax-inst 103

This theorem depends on definitions:  df-ov 65  df-al 116

This theorem is referenced by:  ax4  140  cla4v  142

Copyright terms: Public domain

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