dfex2 - Higher-Order Logic Explorer

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Theorem dfex2 185

Description: Alternative definition of the "there exists" quantifier.

**Hypothesis**
Ref	Expression
dfex2.1

**Assertion**
Ref	Expression
dfex2

Proof of Theorem dfex2 Dummy variable

is distinct from all other variables.

Step	Hyp	Ref	Expression
1		dfex2.1	. . 3
2		wv 58	. . . . 5
3	1, 2	ac 184	. . . 4
4		wtru 40	. . . 4
5	3, 4	adantl 51	. . 3
6	1, 5	exlimdv2 156	. 2
7		wat 180	. . . . 5
8	7, 1	wc 45	. . . 4
9	1, 8	ax4e 158	. . 3
10	9, 4	adantl 51	. 2
11	6, 10	ded 74	1

Colors of variables: type var term

Syntax hints: tv 1

ht 2

hb 3 kc 5

ke 7

kt 8

kbr 9

tex 113

tat 179

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-ac 183

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: (None)