wr4 - Quantum Logic Explorer

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Theorem wr4 199

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 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

Colors of variables: term

Syntax hints: = wb 1 ^⊥ wn 4 ≡ tb 5 1wt 8

This theorem was proved from axioms: ax-a1 30 ax-a2 31 ax-r1 35 ax-r2 36 ax-r4 37 ax-r5 38

This theorem depends on definitions: df-b 39 df-a 40

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