Theorem pm3.21 435

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		pm3.2 434	. 2 ⊢ (ψ → (φ → (ψ ∧ φ)))
2	1	com12 27	1 ⊢ (φ → (ψ → (ψ ∧ φ)))

Syntax hints:   → wi 4   ∧ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  pm3.22  436  iba  489  ancr  532  anc2r  539  pm5.31  571  19.41  1879  2mo  2282