Theorem jao1i 825

Description: Add a disjunct in the antecedent of an implication. (Contributed by Rodolfo Medina, 24-Sep-2010.)

Hypothesis

Ref	Expression
jao1i.1	|- ( ps -> ( ch -> ph ) )

Assertion

Ref	Expression
jao1i	|- ( ( ph \/ ps ) -> ( ch -> ph ) )

Proof of Theorem jao1i

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 |- ( ph -> ( ch -> ph ) )
2		jao1i.1	. 2 |- ( ps -> ( ch -> ph ) )
3	1, 2	jaoi 394	1 |- ( ( ph \/ ps ) -> ( ch -> ph ) )

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:  pm2.64  830  pm2.82  897  nn0enne  15094  dvdsprmpweqnn  15589  dvdsprmpweqle  15590  2lgsoddprmlem3  25139  prtlem14  34159