Theorem pm3.2 139

Description: Join antecedents with conjunction. Theorem *3.2 of [WhiteheadRussell] p. 111. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 12-Nov-2012.) (Proof shortened by Jia Ming, 17-Nov-2020.)

Assertion

Ref	Expression
pm3.2	|- ( ph -> ( ps -> ( ph /\ ps ) ) )

Proof of Theorem pm3.2

Step	Hyp	Ref	Expression
1		ax-ia3 108	1 |- ( ph -> ( ps -> ( ph /\ ps ) ) )

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

This proof depends on axioms:  ax-ia3 108

This theorem is used by:  pm3.21  264  pm3.2i  272  pm3.43i  273  ibar  301  jca  306  jcad  307  ancl  318  imnan  701  pm3.2an3  1207  19.29  1673  r19.26  2677  r19.29  2688  difrab  3507  dmcosseq  5054  lediv2a  9225  ssfzo12  10642  r19.29uz  11758