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	⊢ (𝜑 → (𝜓 → (𝜓 ∧ 𝜑)))

Proof of Theorem pm3.21

Step	Hyp	Ref	Expression
1		pm3.2 139	. 2 ⊢ (𝜓 → (𝜑 → (𝜓 ∧ 𝜑)))
2	1	com12 30	1 ⊢ (𝜑 → (𝜓 → (𝜓 ∧ 𝜑)))

Syntax hints:   → wi 4   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108

This theorem is referenced by:  pm3.22  265  iba  300  ancr  321  anc2r  328  pm5.31  348  xoranor  1377  19.41h  1685  19.41  1686  ltsopr  7591  bj-findis  14582