Theorem pm3.21 436

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		pm3.2 435	. 2 |- ( ps -> ( ph -> ( ps /\ ph ) ) )
2	1	com12 29	1 |- ( ph -> ( ps -> ( ps /\ ph ) ) )

Syntax hints:   -> wi 4   /\ wa 359

This theorem is referenced by:  pm3.22  437  iba  490  ancr  533  anc2r  540  pm5.31  572  19.41  1900  19.41OLD  1901  2mo  2359  smoord  6620  fisupg  7348  winalim2  8564  aalioulem5  20246  musum  20969  chrelat2i  23861  relin01  25187  waj-ax  26157  pm11.71  27565  ssfz12  28089  onfrALTlem2  28570  19.41rg  28575  not12an2impnot1  28597  onfrALTlem2VD  28939  2pm13.193VD  28953  a9e2eqVD  28957  bnj1173  29309  hlrelat2  30138

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 178  df-an 361