Theorem orim1d 776

Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995.)

Hypothesis

Ref	Expression
orim1d.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
orim1d	|- ( ph -> ( ( ps \/ th ) -> ( ch \/ th ) ) )

Proof of Theorem orim1d

Step	Hyp	Ref	Expression
1		orim1d.1	. 2 |- ( ph -> ( ps -> ch ) )
2		idd 21	. 2 |- ( ph -> ( th -> th ) )
3	1, 2	orim12d 775	1 |- ( ph -> ( ( ps \/ th ) -> ( ch \/ th ) ) )

Syntax hints:   -> wi 4   \/ wo 697

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  pm2.38  792  pm2.73  795  pm2.74  796  pm2.8  799  pm2.82  801  unss1  3245  acexmidlemcase  5769  exmidomniim  7013  nn0ge2m1nn  9037  exmidsbthrlem  13217