Theorem orim1i 539

Description: Introduce disjunct to both sides of an implication. (Contributed by NM, 6-Jun-1994.)

Hypothesis

Ref	Expression
orim1i.1	|- ( ph -> ps )

Assertion

Ref	Expression
orim1i	|- ( ( ph \/ ch ) -> ( ps \/ ch ) )

Proof of Theorem orim1i

Step	Hyp	Ref	Expression
1		orim1i.1	. 2 |- ( ph -> ps )
2		id 22	. 2 |- ( ch -> ch )
3	1, 2	orim12i 538	1 |- ( ( ph \/ ch ) -> ( ps \/ ch ) )

Syntax hints:   -> wi 4   \/ wo 383

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-or 385

This theorem is referenced by:  nfntOLDOLD  1783  19.34  1901  r19.45v  3095  nnm1nn0  11334  elfzo0l  12558  xrge0iifhom  29983  bj-andnotim  32573  orfa2  33887  expdioph  37590  ifpimim  37854