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  7405  recgt1i  8656  elnnnn0c  9022  elnnz1  9077  recnz  9144  eluz2b2  9397  elfzp12  9879  cos01gt0  11469  oddnn02np1  11577