Metamath Proof Explorer


Theorem nic-idel

Description: Inference to remove the trailing term. (Contributed by Jeff Hoffman, 17-Nov-2007) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypothesis nic-idel.1
|- ( ph -/\ ( ch -/\ ps ) )
Assertion nic-idel
|- ( ph -/\ ( ch -/\ ch ) )

Proof

Step Hyp Ref Expression
1 nic-idel.1
 |-  ( ph -/\ ( ch -/\ ps ) )
2 nic-id
 |-  ( ch -/\ ( ch -/\ ch ) )
3 2 nic-isw1
 |-  ( ( ch -/\ ch ) -/\ ch )
4 1 nic-imp
 |-  ( ( ( ch -/\ ch ) -/\ ch ) -/\ ( ( ph -/\ ( ch -/\ ch ) ) -/\ ( ph -/\ ( ch -/\ ch ) ) ) )
5 3 4 nic-mp
 |-  ( ph -/\ ( ch -/\ ch ) )