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Theorem axfrege8 36920
Description: Swap antecedents. Identical to pm2.04 87. This demonstrates that Axiom 8 of [Frege1879] p. 35 is redundant.

Proof follows closely proof of pm2.04 87 in http://us.metamath.org/mmsolitaire/pmproofs.txt, but in the style of Frege's 1879 work. (Contributed by RP, 24-Dec-2019.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion
Ref Expression
axfrege8 ((𝜑 → (𝜓𝜒)) → (𝜓 → (𝜑𝜒)))

Proof of Theorem axfrege8
StepHypRef Expression
1 rp-7frege 36914 . 2 ((𝜑 → (𝜓𝜒)) → (𝜓 → ((𝜑𝜓) → (𝜑𝜒))))
2 rp-8frege 36917 . 2 (((𝜑 → (𝜓𝜒)) → (𝜓 → ((𝜑𝜓) → (𝜑𝜒)))) → ((𝜑 → (𝜓𝜒)) → (𝜓 → (𝜑𝜒))))
31, 2ax-mp 5 1 ((𝜑 → (𝜓𝜒)) → (𝜓 → (𝜑𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 36903  ax-frege2 36904
This theorem is referenced by: (None)
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