Theorem imdistani 449

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 ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is used by:  syldanl  453  xoranor  1426  nfan1  1617  sbcof2  1863  difin  3468  difrab  3507  rabsnifsb  3777  opthreg  4705  wessep  4727  fvelimab  5762  elfvmptrab  5805  dffo4  5859  dffo5  5860  ltaddpr  7970  recgt1i  9236  elnnnn0c  9619  elnnz1  9676  recnz  9749  eluz2b2  10018  elfzp12  10522  pfxsuff1eqwrdeq  11492  cos01gt0  12554  oddnn02np1  12671  reumodprminv  13060  ballotfilemfc0  13289  ballotfilemfcc  13290  ballotfilemth  13338  sgrpidmndm  13791  elply2  15978  bj-charfundc  17056