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  4703  wessep  4725  fvelimab  5759  elfvmptrab  5802  dffo4  5856  dffo5  5857  ltaddpr  7964  recgt1i  9228  elnnnn0c  9608  elnnz1  9667  recnz  9739  eluz2b2  10003  elfzp12  10506  pfxsuff1eqwrdeq  11471  cos01gt0  12530  oddnn02np1  12647  reumodprminv  13032  ballotfilemfc0  13232  ballotfilemfcc  13233  ballotfilemth  13281  sgrpidmndm  13733  elply2  15836  bj-charfundc  16834