Theorem pm3.2 434

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.)

Assertion

Ref	Expression
pm3.2	⊢ (φ → (ψ → (φ ∧ ψ)))

Proof of Theorem pm3.2

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ ((φ ∧ ψ) → (φ ∧ ψ))
2	1	ex 423	1 ⊢ (φ → (ψ → (φ ∧ ψ)))

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:  pm3.21  435  pm3.2i  441  pm3.43i  442  ibar  490  jca  518  jcad  519  ancl  529  pm3.2an3  1131  19.29  1596  r19.26  2746  r19.29  2754  difrab  3529