ax12 - Higher-Order Logic Explorer

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Theorem ax12 215

Description: Axiom of Quantifier Introduction. Axiom scheme C9' in [Megill] p. 448 (p. 16 of the preprint). (Contributed by Mario Carneiro, 10-Oct-2014.)

**Assertion**
Ref	Expression
ax12

Distinct variable groups:

Proof of Theorem ax12 Dummy variable

is distinct from all other variables.

Step	Hyp	Ref	Expression
1		wv 64	. . . . . . 7
2		wv 64	. . . . . . 7
3	1, 2	weqi 76	. . . . . 6
4		wv 64	. . . . . . 7
5	3, 4	ax-17 105	. . . . . 6
6	3, 5	isfree 188	. . . . 5
7		wnot 138	. . . . . 6
8		wal 134	. . . . . . 7
9		wv 64	. . . . . . . . 9
10	9, 2	weqi 76	. . . . . . . 8
11	10	wl 66	. . . . . . 7
12	8, 11	wc 50	. . . . . 6
13	7, 12	wc 50	. . . . 5
14	6, 13	adantr 55	. . . 4
15	14	ex 158	. . 3
16	9, 1	weqi 76	. . . . . 6
17	16	wl 66	. . . . 5
18	8, 17	wc 50	. . . 4
19	7, 18	wc 50	. . 3
20	15, 19	adantr 55	. 2
21	20	ex 158	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 120

tim 121

tal 122

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-wctl 31 ax-wctr 32 ax-weq 40 ax-refl 42 ax-eqmp 45 ax-ded 46 ax-wct 47 ax-wc 49 ax-ceq 51 ax-wv 63 ax-wl 65 ax-beta 67 ax-distrc 68 ax-leq 69 ax-distrl 70 ax-wov 71 ax-eqtypi 77 ax-eqtypri 80 ax-hbl1 103 ax-17 105 ax-inst 113 ax-eta 177

This theorem depends on definitions: df-ov 73 df-al 126 df-fal 127 df-an 128 df-im 129 df-not 130

This theorem is referenced by: (None)

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