Theorem nic-bi1

Inference to extract one side of an implication from a definition. (Contributed by Jeff Hoffman, 18-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis
nic-bi1.1
\( \vdash (\varphi \barwedge \psi) \barwedge ((\varphi \barwedge \varphi) \barwedge (\psi \barwedge \psi)) \)
Conclusion
\( \vdash \varphi \barwedge (\psi \barwedge \psi) \)
Proof
l0
nic-bi1.1
\( \vdash (\varphi \barwedge \psi) \barwedge ((\varphi \barwedge \varphi) \barwedge (\psi \barwedge \psi)) \)
nic-id
\( \vdash \varphi \barwedge (\varphi \barwedge \varphi) \)
nic-iimp1 l0 _
nic-isw2 _
\( \vdash \varphi \barwedge (\psi \barwedge \varphi) \)
nic-idel _