Theorem pm3.21 261

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		pm3.2 138	. 2 ⊢ (𝜓 → (𝜑 → (𝜓 ∧ 𝜑)))
2	1	com12 30	1 ⊢ (𝜑 → (𝜓 → (𝜓 ∧ 𝜑)))

Syntax hints:   → wi 4   ∧ wa 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 107

This theorem is referenced by:  pm3.22  262  iba  295  ancr  315  anc2r  322  pm5.31  341  xoranor  1314  19.41h  1621  19.41  1622  ltsopr  7209  bj-findis  12140