Theorem wl-impchain-com-1.2 38210

Description: This theorem is in fact a copy of wl-luk-com12 38193, and repeated here to demonstrate a simple proof scheme. The number '2' in the theorem name indicates that a chain of length 2 is modified.

See wl-impchain-com-1.x 38208 for more information how this proof is generated. (Contributed by Wolf Lammen, 7-Jul-2019.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
wl-impchain-com.1.2.a	⊢ (𝜒 → (𝜓 → 𝜑))

Assertion

Ref	Expression
wl-impchain-com-1.2	⊢ (𝜓 → (𝜒 → 𝜑))

Proof of Theorem wl-impchain-com-1.2

Step	Hyp	Ref	Expression
1		wl-impchain-com.1.2.a	. . . 4 ⊢ (𝜒 → (𝜓 → 𝜑))
2	1	wl-impchain-com-1.1 38209	. . 3 ⊢ (𝜒 → (𝜓 → 𝜑))
3		wl-luk-pm2.04 38202	. . 3 ⊢ ((𝜒 → (𝜓 → 𝜑)) → (𝜓 → (𝜒 → 𝜑)))
4	2, 3	wl-impchain-mp-0 38205	. 2 ⊢ (𝜓 → (𝜒 → 𝜑))
5	4	wl-impchain-com-1.1 38209	1 ⊢ (𝜓 → (𝜒 → 𝜑))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-luk1 38176  ax-luk2 38177  ax-luk3 38178

This theorem is used by:  wl-impchain-com-1.3  38211  wl-impchain-com-2.3  38214  wl-impchain-com-2.4  38215  wl-impchain-com-3.2.1  38216  wl-impchain-a1-2  38219