Theorem pm3.21 435

Description: Join antecedents with conjunction. Theorem *3.21 of [WhiteheadRussell] p. 111. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
pm3.21	|- ( ph -> ( ps -> ( ps /\ ph ) ) )

Proof of Theorem pm3.21

Step	Hyp	Ref	Expression
1		pm3.2 434	. 2 |- ( ps -> ( ph -> ( ps /\ ph ) ) )
2	1	com12 27	1 |- ( ph -> ( ps -> ( ps /\ ph ) ) )

Syntax hints:   -> wi 4   /\ wa 358

This theorem is referenced by:  pm3.22  436  iba  489  ancr  532  anc2r  539  pm5.31  571  19.41  1815  2mo  2221  smoord  6382  fisupg  7105  winalim2  8318  aalioulem5  19716  musum  20431  chrelat2i  22945  relin01  24089  waj-ax  24853  sssu  25141  pm11.71  27596  onfrALTlem2  28311  19.41rg  28316  onfrALTlem2VD  28665  2pm13.193VD  28679  a9e2eqVD  28683  bnj1173  29032  hlrelat2  29592

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8

This theorem depends on definitions:  df-bi 177  df-an 360