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Theorem eta 166

Description: The eta-axiom: a function is determined by its values.

Hypothesis

Ref	Expression
eta.1

Assertion

Ref	Expression
eta

Distinct variable groups:   ,   ,   ,

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

Step	Hyp	Ref	Expression
1		ax-eta 165	. 2
2		weq 38	. . . 4
3		wv 58	. . . . . 6
4		wv 58	. . . . . 6
5	3, 4	wc 45	. . . . 5
6	5	wl 59	. . . 4
7	2, 6, 3	wov 64	. . 3
8		eta.1	. . 3
9	3, 8	weqi 68	. . . . . . 7
10	9	id 25	. . . . . 6
11	3, 4, 10	ceq1 79	. . . . 5
12	5, 11	leq 81	. . . 4
13	2, 6, 3, 12, 10	oveq12 90	. . 3
14	7, 8, 13	cla4v 142	. 2
15	1, 14	syl 16	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  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  ax-eta 165

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

This theorem is referenced by:  cbvf  167  leqf  169  ax11  201  axext  206

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