Theorem orbi1i 763

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 728	. 2 |- ( ( ph \/ ch ) <-> ( ch \/ ph ) )
2		orbi2i.1	. . 3 |- ( ph <-> ps )
3	2	orbi2i 762	. 2 |- ( ( ch \/ ph ) <-> ( ch \/ ps ) )
4		orcom 728	. 2 |- ( ( ch \/ ps ) <-> ( ps \/ ch ) )
5	1, 3, 4	3bitri 206	1 |- ( ( ph \/ ch ) <-> ( ps \/ ch ) )

Syntax hints:   <-> wb 105   \/ wo 708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orbi12i  764  orordi  773  dcan  933  3or6  1323  19.45  1683  sbequilem  1838  unass  3294  frecsuc  6410  nninfwlporlemd  7172  elznn0nn  9269