Theorem w2or 372

Description: Join both sides with disjunction.

Hypotheses

Ref	Expression
w2or.1	(a == b) = 1
w2or.2	(c == d) = 1

Assertion

Ref	Expression
w2or	((a v c) == (b v d)) = 1

Proof of Theorem w2or

Step	Hyp	Ref	Expression
1		w2or.2	. . 3 (c == d) = 1
2	1	wlor 368	. 2 ((a v c) == (a v d)) = 1
3		w2or.1	. . 3 (a == b) = 1
4	3	wr5-2v 366	. 2 ((a v d) == (b v d)) = 1
5	2, 4	wr2 371	1 ((a v c) == (b v d)) = 1

Syntax hints:   = wb 1   == tb 5   v wo 6  1wt 8

This theorem is referenced by:  wcomlem 382  wdf-c1 383  wbctr 410  wcbtr 411  wcomcom5 420  wcomdr 421  wfh1 423  wcom2or 427  ska2 432  wddi2 1105

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-wom 361

This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-le1 130  df-le2 131

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