Theorem simpl2im 386

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 110	. 2 |- ( ( ps /\ ch ) -> ch )
3		simpl2im.2	. 2 |- ( ch -> th )
4	1, 2, 3	3syl 17	1 |- ( ph -> th )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 107

This theorem is referenced by:  rabsnif  3738  ctssdccl  7310  enumct  7314  djuen  7426  ndvdssub  12496  sgrpidmndm  13508  conjsubgen  13870  xmeteq0  15089  xmettri2  15091  metcnpi  15245  metcnpi2  15246  dvbssntrcntop  15414  upgrm  15957  umgrpredgv  16004