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Theorem bj-looinvi 32858
Description: Inference associated with looinv 194. Its associated inference is bj-looinvii 32859. (Contributed by BJ, 30-Mar-2020.)
Hypothesis
Ref Expression
bj-looinvi.1 ((𝜑𝜓) → 𝜓)
Assertion
Ref Expression
bj-looinvi ((𝜓𝜑) → 𝜑)

Proof of Theorem bj-looinvi
StepHypRef Expression
1 bj-looinvi.1 . 2 ((𝜑𝜓) → 𝜓)
2 looinv 194 . 2 (((𝜑𝜓) → 𝜓) → ((𝜓𝜑) → 𝜑))
31, 2ax-mp 5 1 ((𝜓𝜑) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  bj-looinvii  32859
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