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:  ctssdccl  7177  enumct  7181  djuen  7278  ndvdssub  12095  sgrpidmndm  13061  conjsubgen  13408  xmeteq0  14595  xmettri2  14597  metcnpi  14751  metcnpi2  14752  dvbssntrcntop  14920