Theorem wr4 191

Description: Weak R4.

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 114	. . 3 (a ≡ b) = (a⊥ ≡ b⊥ )
2	1	ax-r1 34	. 2 (a⊥ ≡ b⊥ ) = (a ≡ b)
3		wr4.1	. 2 (a ≡ b) = 1
4	2, 3	ax-r2 35	1 (a⊥ ≡ b⊥ ) = 1

Syntax hints:   = wb 1  ^⊥ wn 4   ≡ tb 5  1wt 9

This theorem is referenced by:  wran 351  wr2 353  wcomlem 364  wcbtr 393  wcomdr 403  wfh2 406  wfh3 407  wfh4 408  woml7 419

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-b 38  df-a 39

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