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Theorem bj-mp2c 31535
Description: A double modus ponens inference. (Contributed by BJ, 24-Sep-2019.)
Hypotheses
Ref Expression
bj-mp2c.1 𝜑
bj-mp2c.2 (𝜑𝜓)
bj-mp2c.3 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
bj-mp2c 𝜒

Proof of Theorem bj-mp2c
StepHypRef Expression
1 bj-mp2c.1 . 2 𝜑
2 bj-mp2c.2 . . 3 (𝜑𝜓)
31, 2ax-mp 5 . 2 𝜓
4 bj-mp2c.3 . 2 (𝜑 → (𝜓𝜒))
51, 3, 4mp2 9 1 𝜒
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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