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Theorem imp 147

Description: Importation deduction.

Hypotheses

Ref	Expression
imp.1
imp.2
imp.3

Assertion

Ref	Expression
imp

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Proof of Theorem imp

Step	Hyp	Ref	Expression
1		imp.2	. 2
2		imp.3	. . . 4
3	2	ax-cb1 29	. . 3
4		imp.1	. . 3
5	3, 4	simpr 23	. 2
6	2, 4	adantr 50	. 2
7	1, 5, 6	mpd 146	1

Colors of variables: type var term

Syntax hints:  hb 3  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:  con2d  151  exlimdv  157  alnex  174  notnot  187  ax3  192

Copyright terms: Public domain

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