Theorem rp-simp2 38087

Description: Simplification of triple conjunction. Identical to simp2 1062. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
rp-simp2	|- ( ( ph /\ ps /\ ch ) -> ps )

Proof of Theorem rp-simp2

Step	Hyp	Ref	Expression
1		rp-simp2-frege 38086	. 2 |- ( ph -> ( ps -> ( ch -> ps ) ) )
2	1	3imp 1256	1 |- ( ( ph /\ ps /\ ch ) -> ps )

Syntax hints:   -> wi 4   /\ w3a 1037

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege1 38084

This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1039

This theorem is referenced by:  ntrclsk3  38368