Theorem wlan 352

Description: Weak orthomodular law.

Hypothesis

Ref	Expression
wlan.1	(a == b) = 1

Assertion

Ref	Expression
wlan	((c ^ a) == (c ^ b)) = 1

Proof of Theorem wlan

Step	Hyp	Ref	Expression
1		ancom 68	. . 3 (c ^ a) = (a ^ c)
2		ancom 68	. . 3 (c ^ b) = (b ^ c)
3	1, 2	2bi 91	. 2 ((c ^ a) == (c ^ b)) = ((a ^ c) == (b ^ c))
4		wlan.1	. . 3 (a == b) = 1
5	4	wran 351	. 2 ((a ^ c) == (b ^ c)) = 1
6	3, 5	ax-r2 35	1 ((c ^ a) == (c ^ b)) = 1

Syntax hints:   = wb 1   == tb 5   ^ wa 7  1wt 9

This theorem is referenced by:  w2an 355  wleoa 358  wom4 362  wcomlem 364  wletr 378  wlbtr 380  wcbtr 393  wcomcom2 397  wcom3ii 401  wfh1 405  wfh2 406  wlem14 412

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a4 32  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37  ax-wom 343

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i1 43  df-i2 44  df-le1 122  df-le2 123

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