Theorem orbi1i 715

Description: Inference adding a right disjunct to both sides of a logical equivalence. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
orbi2i.1	|- ( ph <-> ps )

Assertion

Ref	Expression
orbi1i	|- ( ( ph \/ ch ) <-> ( ps \/ ch ) )

Proof of Theorem orbi1i

Step	Hyp	Ref	Expression
1		orcom 682	. 2 |- ( ( ph \/ ch ) <-> ( ch \/ ph ) )
2		orbi2i.1	. . 3 |- ( ph <-> ps )
3	2	orbi2i 714	. 2 |- ( ( ch \/ ph ) <-> ( ch \/ ps ) )
4		orcom 682	. 2 |- ( ( ch \/ ps ) <-> ( ps \/ ch ) )
5	1, 3, 4	3bitri 204	1 |- ( ( ph \/ ch ) <-> ( ps \/ ch ) )

Syntax hints:   <-> wb 103   \/ wo 664

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  orbi12i  716  orordi  725  dcan  880  3or6  1259  19.45  1618  sbequilem  1766  unass  3157  frecsuc  6172  elznn0nn  8764