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Theorem prvlem2 32226
Description: An elementary property of the provability predicate. (Contributed by BJ, 3-Apr-2019.)
Hypothesis
Ref Expression
prvlem2.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
prvlem2 (Prv 𝜑 → (Prv 𝜓 → Prv 𝜒))

Proof of Theorem prvlem2
StepHypRef Expression
1 prvlem2.1 . . 3 (𝜑 → (𝜓𝜒))
21prvlem1 32225 . 2 (Prv 𝜑 → Prv (𝜓𝜒))
3 ax-prv2 32223 . 2 (Prv (𝜓𝜒) → (Prv 𝜓 → Prv 𝜒))
42, 3syl 17 1 (Prv 𝜑 → (Prv 𝜓 → Prv 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  Prv cprvb 32221
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-prv1 32222  ax-prv2 32223
This theorem is referenced by:  bj-babygodel  32227  bj-babylob  32228
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