Theorem pm3.21 437

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		pm3.2 436	. 2 |- ( ps -> ( ph -> ( ps /\ ph ) ) )
2	1	com12 29	1 |- ( ph -> ( ps -> ( ps /\ ph ) ) )

Syntax hints:   -> wi 6   /\ wa 360

This theorem is referenced by:  pm3.22  438  iba  491  ancr  534  anc2r  541  pm5.31  574  19.41  1819  2mo  2222  smoord  6377  fisupg  7100  winalim2  8313  aalioulem5  19710  musum  20425  chrelat2i  22937  relin01  23492  waj-ax  24260  sssu  24540  pm11.71  26995  onfrALTlem2  27582  19.41rg  27587  onfrALTlem2VD  27933  2pm13.193VD  27947  a9e2eqVD  27951  bnj1173  28299  hlrelat2  28859

This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10

This theorem depends on definitions:  df-bi 179  df-an 362