Theorem jao1i 808

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 728	1 |- ( ( ph \/ ps ) -> ( ch -> ph ) )

This proof depends on syntax axioms:   -> wi 4   \/ wo 720

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721

This proof depends on definitions:  df-bi 117

This theorem is used by:  nn0enne  12669  dvdsprmpweqnn  13115  dvdsprmpweqle  13116  2lgs  16223  2lgsoddprmlem3  16230