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  1419  nfan1  1610  sbcof2  1856  difin  3441  difrab  3478  opthreg  4647  wessep  4669  fvelimab  5689  elfvmptrab  5729  dffo4  5782  dffo5  5783  ltaddpr  7780  recgt1i  9041  elnnnn0c  9410  elnnz1  9465  recnz  9536  eluz2b2  9794  elfzp12  10291  pfxsuff1eqwrdeq  11226  cos01gt0  12269  oddnn02np1  12386  reumodprminv  12771  sgrpidmndm  13448  elply2  15403  bj-charfundc  16129