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Theorem wl-ja 32893
Description: Inference joining the antecedents of two premises. Copy of ja 173 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
wl-ja.1 𝜑𝜒)
wl-ja.2 (𝜓𝜒)
Assertion
Ref Expression
wl-ja ((𝜑𝜓) → 𝜒)

Proof of Theorem wl-ja
StepHypRef Expression
1 wl-ja.1 . . . 4 𝜑𝜒)
21wl-con1i 32892 . . 3 𝜒𝜑)
3 wl-ja.2 . . . 4 (𝜓𝜒)
43wl-imim2i 32885 . . 3 ((𝜑𝜓) → (𝜑𝜒))
52, 4wl-syl5 32879 . 2 ((𝜑𝜓) → (¬ 𝜒𝜒))
65wl-pm2.18d 32880 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-luk1 32873  ax-luk2 32874  ax-luk3 32875
This theorem is referenced by:  wl-ax2  32896
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