Theorem xorbi12i 1274

Description: Equality property for XOR. (Contributed by Mario Carneiro, 4-Sep-2016.)

Hypotheses

Ref	Expression
xorbi12.1	|- ( ph <-> ps )
xorbi12.2	|- ( ch <-> th )

Assertion

Ref	Expression
xorbi12i	|- ( ( ph \/_ ch ) <-> ( ps \/_ th ) )

Proof of Theorem xorbi12i

Step	Hyp	Ref	Expression
1		xorbi12.1	. . . 4 |- ( ph <-> ps )
2	1	a1i 9	. . 3 |- ( T. -> ( ph <-> ps ) )
3		xorbi12.2	. . . 4 |- ( ch <-> th )
4	3	a1i 9	. . 3 |- ( T. -> ( ch <-> th ) )
5	2, 4	xorbi12d 1273	. 2 |- ( T. -> ( ( ph \/_ ch ) <-> ( ps \/_ th ) ) )
6	5	trud 1252	1 |- ( ( ph \/_ ch ) <-> ( ps \/_ th ) )

Syntax hints:   <-> wb 98   T. wtru 1244   \/_ wxo 1266

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 630

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-xor 1267

This theorem is referenced by: (None)