Theorem imdistani 445

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 329	. 2 |- ( ph -> ( ps -> ( ph /\ ch ) ) )
3	2	imp 124	1 |- ( ( ph /\ ps ) -> ( ph /\ ch ) )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is referenced by:  syldanl  449  xoranor  1388  nfan1  1578  sbcof2  1824  difin  3401  difrab  3438  opthreg  4593  wessep  4615  fvelimab  5620  elfvmptrab  5660  dffo4  5713  dffo5  5714  ltaddpr  7681  recgt1i  8942  elnnnn0c  9311  elnnz1  9366  recnz  9436  eluz2b2  9694  elfzp12  10191  cos01gt0  11945  oddnn02np1  12062  reumodprminv  12447  sgrpidmndm  13122  elply2  15055  bj-charfundc  15538