Theorem wl-impchain-com-1.4 38160

Description: This theorem is in fact a copy of com14 97, and repeated here to demonstrate a simple proof scheme. The number '4' in the theorem name indicates that a chain of length 4 is modified.

See wl-impchain-com-1.x 38156 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-1.4.h1	⊢ (𝜂 → (𝜃 → (𝜒 → (𝜓 → 𝜑))))

Assertion

Ref	Expression
wl-impchain-com-1.4	⊢ (𝜓 → (𝜃 → (𝜒 → (𝜂 → 𝜑))))

Proof of Theorem wl-impchain-com-1.4

Step	Hyp	Ref	Expression
1		wl-impchain-com-1.4.h1	. . . 4 ⊢ (𝜂 → (𝜃 → (𝜒 → (𝜓 → 𝜑))))
2	1	wl-impchain-com-1.3 38159	. . 3 ⊢ (𝜒 → (𝜃 → (𝜂 → (𝜓 → 𝜑))))
3		wl-luk-pm2.04 38150	. . 3 ⊢ ((𝜂 → (𝜓 → 𝜑)) → (𝜓 → (𝜂 → 𝜑)))
4	2, 3	wl-impchain-mp-2 38155	. 2 ⊢ (𝜒 → (𝜃 → (𝜓 → (𝜂 → 𝜑))))
5	4	wl-impchain-com-1.3 38159	1 ⊢ (𝜓 → (𝜃 → (𝜒 → (𝜂 → 𝜑))))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-luk1 38124  ax-luk2 38125  ax-luk3 38126

This theorem is used by:  wl-impchain-com-2.4  38163