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Theorem bj-mp2c 33083
Description: A double modus ponens inference. (Contributed by BJ, 24-Sep-2019.)
Hypotheses
Ref Expression
bj-mp2c.1  |-  ph
bj-mp2c.2  |-  ( ph  ->  ps )
bj-mp2c.3  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
bj-mp2c  |-  ch

Proof of Theorem bj-mp2c
StepHypRef Expression
1 bj-mp2c.1 . 2  |-  ph
2 bj-mp2c.2 . . 3  |-  ( ph  ->  ps )
31, 2ax-mp 5 . 2  |-  ps
4 bj-mp2c.3 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
51, 3, 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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