Theorem imdistani 441

Description: Distribution of implication with conjunction. (Contributed by NM, 1-Aug-1994.)

Hypothesis

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

Assertion

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

Proof of Theorem imdistani

Step	Hyp	Ref	Expression
1		imdistani.1	. . 3 |- ( ph -> ( ps -> ch ) )
2	1	anc2li 327	. 2 |- ( ph -> ( ps -> ( ph /\ ch ) ) )
3	2	imp 123	1 |- ( ( ph /\ ps ) -> ( ph /\ ch ) )

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 is referenced by:  xoranor  1355  nfan1  1543  sbcof2  1782  difin  3313  difrab  3350  opthreg  4471  wessep  4492  fvelimab  5477  elfvmptrab  5516  dffo4  5568  dffo5  5569  ltaddpr  7412  recgt1i  8663  elnnnn0c  9029  elnnz1  9084  recnz  9151  eluz2b2  9404  elfzp12  9886  cos01gt0  11476  oddnn02np1  11584