Theorem imdistanda 445

Description: Distribution of implication with conjunction (deduction version with conjoined antecedent). (Contributed by Jeff Madsen, 19-Jun-2011.)

Hypothesis

Ref	Expression
imdistanda.1	|- ( ( ph /\ ps ) -> ( ch -> th ) )

Assertion

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

Proof of Theorem imdistanda

Step	Hyp	Ref	Expression
1		imdistanda.1	. . 3 |- ( ( ph /\ ps ) -> ( ch -> th ) )
2	1	ex 114	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	imdistand 444	1 |- ( ph -> ( ( ps /\ ch ) -> ( ps /\ th ) ) )

Syntax hints:   -> wi 4   /\ wa 103

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

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  fzind  9306  uzss  9486  exbtwnzlemshrink  10184  rebtwn2zlemshrink  10189  cau3lem  11056  iscnp4  12858  cnntr  12865