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Theorem simpl2im 383
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
StepHypRef Expression
1 simpl2im.1 . 2  |-  ( ph  ->  ( ps  /\  ch ) )
2 simpr 109 . 2  |-  ( ( ps  /\  ch )  ->  ch )
3 simpl2im.2 . 2  |-  ( ch 
->  th )
41, 2, 33syl 17 1  |-  ( ph  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106
This theorem is referenced by:  ctssdccl  6996  enumct  7000  djuen  7072  ndvdssub  11638  xmeteq0  12542  xmettri2  12544  metcnpi  12698  metcnpi2  12699  dvbssntrcntop  12836
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