Theorem orim1i 760

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 19	. 2 |- ( ch -> ch )
3	1, 2	orim12i 759	1 |- ( ( ph \/ ch ) -> ( ps \/ ch ) )

Syntax hints:   -> wi 4   \/ 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:  19.34  1684  dveeq2or  1816  sbequilem  1838  sbequi  1839  dvelimALT  2010  dvelimfv  2011  dvelimor  2018  r19.45av  2637  acexmidlemcase  5872  omniwomnimkv  7167  nnm1nn0  9219  prmdc  12132  triap  14862