Theorem imdistanda 437

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 113	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	imdistand 436	1 |- ( ph -> ( ( ps /\ ch ) -> ( ps /\ th ) ) )

Syntax hints:   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  fzind  8859  uzss  9037  exbtwnzlemshrink  9656  rebtwn2zlemshrink  9661  cau3lem  10543