Theorem ud3lem0c 279

Description: Lemma for unified disjunction. (Contributed by NM, 22-Nov-1997.)

Assertion

Ref	Expression
ud3lem0c	(a →3 b)⊥ = (((a ∪ b⊥ ) ∩ (a ∪ b)) ∩ (a⊥ ∪ (a ∩ b⊥ )))

Proof of Theorem ud3lem0c

Step	Hyp	Ref	Expression
1		ni31 250	1 (a →3 b)⊥ = (((a ∪ b⊥ ) ∩ (a ∪ b)) ∩ (a⊥ ∪ (a ∩ b⊥ )))

This proof depends on syntax axioms:   = wb 1  ^⊥ wn 4   ∪ wo 6   ∩ wa 7   →₃ wi3 14

This proof depends on axioms:  ax-a1 30  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This proof depends on definitions:  df-a 40  df-i3 46

This theorem is used by:  ud3lem1a  566  ud3lem1b  567  ud3lem1c  568  ud3lem3a  572  ud3lem3b  573  ud3lem3c  574  ud3lem3  576  u3lem14mp  794