ax12 - Higher-Order Logic Explorer

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Theorem ax12 202

Description: Axiom of Quantifier Introduction. Axiom scheme C9' in [Megill] p. 448 (p. 16 of the preprint).

**Assertion**
Ref	Expression
ax12

Proof of Theorem ax12 Dummy variable

is distinct from all other variables.

Step	Hyp	Ref	Expression
1		wv 58	. . . . . . 7
2		wv 58	. . . . . . 7
3	1, 2	weqi 68	. . . . . 6
4		wv 58	. . . . . . 7
5	3, 4	ax-17 95	. . . . . 6
6	3, 5	isfree 176	. . . . 5
7		wnot 128	. . . . . 6
8		wal 124	. . . . . . 7
9		wv 58	. . . . . . . . 9
10	9, 2	weqi 68	. . . . . . . 8
11	10	wl 59	. . . . . . 7
12	8, 11	wc 45	. . . . . 6
13	7, 12	wc 45	. . . . 5
14	6, 13	adantr 50	. . . 4
15	14	ex 148	. . 3
16	9, 1	weqi 68	. . . . . 6
17	16	wl 59	. . . . 5
18	8, 17	wc 45	. . . 4
19	7, 18	wc 45	. . 3
20	15, 19	adantr 50	. 2
21	20	ex 148	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

tne 110

tim 111

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-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

This theorem is referenced by: (None)