Theorem pm3.2

Description: Join antecedents with conjunction ("conjunction introduction"). Theorem *3.2 of WhiteheadRussell p. 111. Its associated inference is pm3.2i and its associated deduction is jca (and the double deduction is jcad ). See pm3.2im for a version using only implication and negation. (Contributed by NM, 5-Jan-1993) (Proof shortened by Wolf Lammen, 12-Nov-2012)

	Ref	Expression
Assertion	pm3.2	$$⊢\phi \to \left(\psi \to \left(\phi \wedge \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\left(\phi \wedge \psi \right)\to \left(\phi \wedge \psi \right)$$
2	1	ex	$$⊢\phi \to \left(\psi \to \left(\phi \wedge \psi \right)\right)$$