Theorem xorbi12d 1271

Description: Deduction joining two equivalences to form equivalence of exclusive-or. (Contributed by Jim Kingdon, 7-Oct-2018.)

Hypotheses

Ref	Expression
xorbi12d.1	|- (ph -> (ps <-> ch))
xorbi12d.2	|- (ph -> (th <-> ta))

Assertion

Ref	Expression
xorbi12d	|- (ph -> ((ps \/_ th) <-> (ch \/_ ta)))

Proof of Theorem xorbi12d

Step	Hyp	Ref	Expression
1		xorbi12d.1	. . 3 |- (ph -> (ps <-> ch))
2	1	xorbi1d 1270	. 2 |- (ph -> ((ps \/_ th) <-> (ch \/_ th)))
3		xorbi12d.2	. . 3 |- (ph -> (th <-> ta))
4	3	xorbi2d 1269	. 2 |- (ph -> ((ch \/_ th) <-> (ch \/_ ta)))
5	2, 4	bitrd 177	1 |- (ph -> ((ps \/_ th) <-> (ch \/_ ta)))

Syntax hints:   -> wi 4   <-> wb 98   \/_ wxo 1265

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629

This theorem depends on definitions:  df-bi 110  df-xor 1266

This theorem is referenced by:  anxordi  1288  rpnegap  8390