Theorem wcom0 389

Description: Commutation with 0. Kalmbach 83 p. 20.

Assertion

Ref	Expression
wcom0	C (a, 0) = 1

Proof of Theorem wcom0

Step	Hyp	Ref	Expression
1		comm0 170	. . . 4 a C 0
2	1	df-c2 125	. . 3 a = ((a ∩ 0) ∪ (a ∩ 0⊥ ))
3	2	bi1 110	. 2 (a ≡ ((a ∩ 0) ∪ (a ∩ 0⊥ ))) = 1
4	3	wdf-c1 365	1 C (a, 0) = 1

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6   ∩ wa 7  1wt 9  0wf 10   C wcmtr 28

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a4 32  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37  ax-wom 343

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i1 43  df-i2 44  df-le 121  df-le1 122  df-le2 123  df-c1 124  df-c2 125  df-cmtr 126

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