Theorem simplbi2com

Description: A deduction eliminating a conjunct, similar to simplbi2 . (Contributed by Alan Sare, 22-Jul-2012) (Proof shortened by Wolf Lammen, 10-Nov-2012)

	Ref	Expression
Hypothesis	simplbi2com.1	$$⊢\phi \leftrightarrow \left(\psi \wedge \chi \right)$$
Assertion	simplbi2com	$$⊢\chi \to \left(\psi \to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		simplbi2com.1	$$⊢\phi \leftrightarrow \left(\psi \wedge \chi \right)$$
2	1	simplbi2	$$⊢\psi \to \left(\chi \to \phi \right)$$
3	2	com12	$$⊢\chi \to \left(\psi \to \phi \right)$$