Theorem pm3.21 264

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		pm3.2 139	. 2 |- ( ps -> ( ph -> ( ps /\ ph ) ) )
2	1	com12 30	1 |- ( ph -> ( ps -> ( ps /\ ph ) ) )

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-ia3 108

This theorem is used by:  pm3.22  265  iba  300  ancr  321  anc2r  328  pm5.31  348  xoranor  1426  19.41h  1737  19.41  1738  ltsopr  7963  bj-findis  17005