Theorem thm3.8i5 1081

Description: (Contributed by Roy F. Longton, 29-Jun-2005.) (Revised by Roy F. Longton, 31-Mar-2011.)

Hypothesis

Ref	Expression
thm3.8i5.1	(a ≡5 b) = 1

Assertion

Ref	Expression
thm3.8i5	((a ∪ c) ≡5 (b ∪ c)) = 1

Proof of Theorem thm3.8i5

Step	Hyp	Ref	Expression
1		thm3.8i5.1	. 2 (a ≡5 b) = 1
2	1	lem3.4.6 1079	1 ((a ∪ c) ≡5 (b ∪ c)) = 1

Syntax hints:   = wb 1   ∪ wo 6  1wt 8   ≡₅ wid5 22

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-wom 361

This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i0 43  df-i1 44  df-i2 45  df-le1 130  df-le2 131  df-id5 1047  df-b1 1048

This theorem is referenced by: (None)