ax7 - Higher-Order Logic Explorer

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Theorem ax7 196

Description: Axiom of Quantifier Commutation. Axiom scheme C6' in [Megill] p. 448 (p. 16 of the preprint).

**Hypothesis**
Ref	Expression
ax7.1

**Assertion**
Ref	Expression
ax7

Proof of Theorem ax7 Dummy variable

is distinct from all other variables.

Step	Hyp	Ref	Expression
1		wal 124	. . . . . . . 8
2		ax7.1	. . . . . . . . 9
3	2	wl 59	. . . . . . . 8
4	1, 3	wc 45	. . . . . . 7
5	4	ax4 140	. . . . . 6
6	2	ax4 140	. . . . . 6
7	5, 6	syl 16	. . . . 5
8	4	wl 59	. . . . . 6
9		wv 58	. . . . . 6
10	1, 9	ax-17 95	. . . . . 6
11	4, 9	ax-hbl1 93	. . . . . 6
12	1, 8, 9, 10, 11	hbc 100	. . . . 5
13	7, 12	alrimi 170	. . . 4
14	1, 9	ax-17 95	. . . . 5
15	2, 9	ax-hbl1 93	. . . . . . 7
16	1, 3, 9, 14, 15	hbc 100	. . . . . 6
17	4, 9, 16	hbl 102	. . . . 5
18	1, 8, 9, 14, 17	hbc 100	. . . 4
19	13, 18	alrimi 170	. . 3
20		wtru 40	. . 3
21	19, 20	adantl 51	. 2
22	21	ex 148	1

Colors of variables: type var term

Syntax hints: tv 1

ht 2

hb 3 kc 5

kl 6

kt 8

kbr 9

wffMMJ2 11 wffMMJ2t 12

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-an 118 df-im 119

This theorem is referenced by: (None)