Theorem wr4 199

Description: Weak R4. (Contributed by NM, 2-Sep-1997.)

Hypothesis

Ref	Expression
wr4.1	(a ≡ b) = 1

Assertion

Ref	Expression
wr4	(a⊥ ≡ b⊥ ) = 1

Proof of Theorem wr4

Step	Hyp	Ref	Expression
1		conb 122	. . 3 (a ≡ b) = (a⊥ ≡ b⊥ )
2	1	ax-r1 35	. 2 (a⊥ ≡ b⊥ ) = (a ≡ b)
3		wr4.1	. 2 (a ≡ b) = 1
4	2, 3	ax-r2 36	1 (a⊥ ≡ b⊥ ) = 1

This proof depends on syntax axioms:   = wb 1  ^⊥ wn 4   ≡ tb 5  1wt 8

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-b 39  df-a 40

This theorem is used by:  wran  369  wr2  371  wcomlem  382  wcbtr  411  wcomdr  421  wfh2  424  wfh3  425  wfh4  426  woml7  437