Theorem simpl2im 658

Description: Implication from an eliminated conjunct implied by the antecedent. (Contributed by BJ/AV, 5-Apr-2021.)

Hypotheses

Ref	Expression
simpl2im.1	|- ( ph -> ( ps /\ ch ) )
simpl2im.2	|- ( ch -> th )

Assertion

Ref	Expression
simpl2im	|- ( ph -> th )

Proof of Theorem simpl2im

Step	Hyp	Ref	Expression
1		simpl2im.1	. 2 |- ( ph -> ( ps /\ ch ) )
2		simpr 477	. 2 |- ( ( ps /\ ch ) -> ch )
3		simpl2im.2	. 2 |- ( ch -> th )
4	1, 2, 3	3syl 18	1 |- ( ph -> th )

Syntax hints:   -> wi 4   /\ wa 384

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

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

This theorem is referenced by:  dvdsaddre2b  15029  ndvdssub  15133  nbgrcl  26233  usgr2trlncrct  26698  wwlksnextproplem3  26806  erclwwlksnsym  26947  erclwwlksntr  26948  numclwlk2lem2f  27236  gneispaceel  38441  gneispacess  38443