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Theorem ex-natded5.2i 27590
Description: The same as ex-natded5.2 27588 and ex-natded5.2-2 27589 but with no context. (Contributed by Mario Carneiro, 9-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ex-natded5.2i.1 ((𝜓𝜒) → 𝜃)
ex-natded5.2i.2 (𝜒𝜓)
ex-natded5.2i.3 𝜒
Assertion
Ref Expression
ex-natded5.2i 𝜃

Proof of Theorem ex-natded5.2i
StepHypRef Expression
1 ex-natded5.2i.3 . . . 4 𝜒
2 ex-natded5.2i.2 . . . 4 (𝜒𝜓)
31, 2ax-mp 5 . . 3 𝜓
43, 1pm3.2i 458 . 2 (𝜓𝜒)
5 ex-natded5.2i.1 . 2 ((𝜓𝜒) → 𝜃)
64, 5ax-mp 5 1 𝜃
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 198  df-an 385
This theorem is referenced by: (None)
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