Theorem simplbda

Description: Deduction eliminating a conjunct. (Contributed by NM, 22-Oct-2007)

	Ref	Expression
Hypothesis	simplbda.1	$$⊢\phi \to \left(\psi \leftrightarrow \left(\chi \wedge \theta \right)\right)$$
Assertion	simplbda	$$⊢\left(\phi \wedge \psi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		simplbda.1	$$⊢\phi \to \left(\psi \leftrightarrow \left(\chi \wedge \theta \right)\right)$$
2	1	biimpa	$$⊢\left(\phi \wedge \psi \right)\to \left(\chi \wedge \theta \right)$$
3	2	simprd	$$⊢\left(\phi \wedge \psi \right)\to \theta$$