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Theorem ax2 191

Description: Axiom Frege. Axiom A2 of [Margaris] p. 49.

Hypotheses

Ref	Expression
ax1.1
ax1.2
ax2.3

Assertion

Ref	Expression
ax2

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Proof of Theorem ax2

Step	Hyp	Ref	Expression
1		ax2.3	. . . . . 6
2		ax1.2	. . . . . . 7
3		wim 127	. . . . . . . . . 10
4		ax1.1	. . . . . . . . . 10
5	3, 2, 1	wov 64	. . . . . . . . . 10
6	3, 4, 5	wov 64	. . . . . . . . 9
7	3, 4, 2	wov 64	. . . . . . . . 9
8	6, 7	wct 44	. . . . . . . 8
9	8, 4	simpr 23	. . . . . . 7
10	8, 4	simpl 22	. . . . . . . 8
11	10	simprd 36	. . . . . . 7
12	2, 9, 11	mpd 146	. . . . . 6
13	10	simpld 35	. . . . . . 7
14	5, 9, 13	mpd 146	. . . . . 6
15	1, 12, 14	mpd 146	. . . . 5
16	15	ex 148	. . . 4
17	16	ex 148	. . 3
18		wtru 40	. . 3
19	17, 18	adantl 51	. 2
20	19	ex 148	1

Colors of variables: type var term

Syntax hints:  hb 3  kt 8  kbr 9  kct 10   wffMMJ2 11  wffMMJ2t 12   tim 111

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

This theorem depends on definitions:  df-ov 65  df-an 118  df-im 119

This theorem is referenced by: (None)

Copyright terms: Public domain

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