Theorem w2or 372

Description: Join both sides with disjunction. (Contributed by NM, 13-Oct-1997.)

Hypotheses

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

Assertion

Ref	Expression
w2or	((a ∪ c) ≡ (b ∪ d)) = 1

Proof of Theorem w2or

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

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

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

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  1108