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Theorem wl-pm2.04 32239
Description: Swap antecedents. Theorem *2.04 of [WhiteheadRussell] p. 100. This was the third axiom in Frege's logic system, specifically Proposition 8 of [Frege1879] p. 35. Copy of pm2.04 87 with a different proof. (Contributed by Wolf Lammen, 7-Jul-2019.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
wl-pm2.04 ((𝜑 → (𝜓𝜒)) → (𝜓 → (𝜑𝜒)))

Proof of Theorem wl-pm2.04
StepHypRef Expression
1 wl-ax1 32228 . 2 (𝜓 → (𝜑𝜓))
2 wl-ax2 32236 . 2 ((𝜑 → (𝜓𝜒)) → ((𝜑𝜓) → (𝜑𝜒)))
31, 2wl-syl5 32219 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-luk1 32213  ax-luk2 32214  ax-luk3 32215
This theorem is referenced by:  wl-impchain-com-1.2  32247  wl-impchain-com-1.3  32248  wl-impchain-com-1.4  32249
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