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  1422  nfan1  1613  sbcof2  1858  difin  3446  difrab  3483  rabsnifsb  3741  opthreg  4660  wessep  4682  fvelimab  5711  elfvmptrab  5751  dffo4  5803  dffo5  5804  ltaddpr  7860  recgt1i  9120  elnnnn0c  9489  elnnz1  9546  recnz  9617  eluz2b2  9881  elfzp12  10379  pfxsuff1eqwrdeq  11329  cos01gt0  12387  oddnn02np1  12504  reumodprminv  12889  sgrpidmndm  13566  elply2  15529  bj-charfundc  16507