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Theorem wl-syl6 33591
Description: A syllogism rule of inference. The second premise is used to replace the consequent of the first premise. Copy of syl6 35 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
wl-syl6.1 (𝜑 → (𝜓𝜒))
wl-syl6.2 (𝜒𝜃)
Assertion
Ref Expression
wl-syl6 (𝜑 → (𝜓𝜃))

Proof of Theorem wl-syl6
StepHypRef Expression
1 wl-syl6.1 . 2 (𝜑 → (𝜓𝜒))
2 wl-syl6.2 . . 3 (𝜒𝜃)
32wl-imim2i 33590 . 2 ((𝜓𝜒) → (𝜓𝜃))
41, 3wl-syl 33583 1 (𝜑 → (𝜓𝜃))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-luk1 33578  ax-luk2 33579  ax-luk3 33580
This theorem is referenced by:  wl-ax3  33592  wl-pm2.27  33594
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