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Theorem gt1 492

Description: Part of Lemma 1 from Gaisi Takeuti, "Quantum Set Theory".

Hypotheses

Ref	Expression
gt1.1
gt1.2
gt1.3

Assertion

Ref	Expression
gt1

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Proof of Theorem gt1

Step	Hyp	Ref	Expression
1		gt1.1	. 2
2		gt1.2	. . . . . 6
3	2	lecom 180	. . . . 5
4	3	comcom 453	. . . 4
5		gt1.3	. . . . . . 7
6	5	lecom 180	. . . . . 6
7	6	comcom7 460	. . . . 5
8	7	comcom 453	. . . 4
9	4, 8	com2or 483	. . 3
10	9	comcom 453	. 2
11	1, 10	bctr 181	1

Colors of variables: term

Syntax hints:   wb 1   wle 2   wc 3  wn 4   wo 6

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439

This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-le1 130  df-le2 131  df-c1 132  df-c2 133

This theorem is referenced by: (None)

Copyright terms: Public domain

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