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Theorem mp2b 9
Description: A double modus ponens inference. (Contributed by Mario Carneiro, 24-Jan-2013.)
Hypotheses
Ref Expression
mp2b.1 φ
mp2b.2 (φψ)
mp2b.3 (ψχ)
Assertion
Ref Expression
mp2b χ

Proof of Theorem mp2b
StepHypRef Expression
1 mp2b.1 . . 3 φ
2 mp2b.2 . . 3 (φψ)
31, 2ax-mp 8 . 2 ψ
4 mp2b.3 . 2 (ψχ)
53, 4ax-mp 8 1 χ
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 8
This theorem is referenced by:  equid  1676  eqvinc  2966  nfunv  5138  funres11  5164  fundmen  6043  xpsnen  6049  xpassen  6057  ncssfin  6151  ce0addcnnul  6179
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