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Theorem bj-mp2d 33084
Description: A double modus ponens inference. (Contributed by BJ, 24-Sep-2019.)
Hypotheses
Ref Expression
bj-mp2d.1  |-  ph
bj-mp2d.2  |-  ( ph  ->  ps )
bj-mp2d.3  |-  ( ps 
->  ( ph  ->  ch ) )
Assertion
Ref Expression
bj-mp2d  |-  ch

Proof of Theorem bj-mp2d
StepHypRef Expression
1 bj-mp2d.1 . . 3  |-  ph
2 bj-mp2d.2 . . 3  |-  ( ph  ->  ps )
31, 2ax-mp 5 . 2  |-  ps
4 bj-mp2d.3 . 2  |-  ( ps 
->  ( ph  ->  ch ) )
53, 1, 4mp2 9 1  |-  ch
Colors of variables: wff setvar class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-mp 5
This theorem is referenced by: (None)
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