Theorem wl-impchain-com-1.3 32452

Description: This theorem is in fact a copy of com13 86, and repeated here to demonstrate a simple proof scheme. The number '3' in the theorem name indicates that a chain of length 3 is modified.

See wl-impchain-com-1.x 32449 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-1.3.h1	⊢ (𝜃 → (𝜒 → (𝜓 → 𝜑)))

Assertion

Ref	Expression
wl-impchain-com-1.3	⊢ (𝜓 → (𝜒 → (𝜃 → 𝜑)))

Proof of Theorem wl-impchain-com-1.3

Step	Hyp	Ref	Expression
1		wl-impchain-com-1.3.h1	. . . 4 ⊢ (𝜃 → (𝜒 → (𝜓 → 𝜑)))
2	1	wl-impchain-com-1.2 32451	. . 3 ⊢ (𝜒 → (𝜃 → (𝜓 → 𝜑)))
3		wl-pm2.04 32443	. . 3 ⊢ ((𝜃 → (𝜓 → 𝜑)) → (𝜓 → (𝜃 → 𝜑)))
4	2, 3	wl-impchain-mp-1 32447	. 2 ⊢ (𝜒 → (𝜓 → (𝜃 → 𝜑)))
5	4	wl-impchain-com-1.2 32451	1 ⊢ (𝜓 → (𝜒 → (𝜃 → 𝜑)))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 32417  ax-luk2 32418  ax-luk3 32419

This theorem is referenced by:  wl-impchain-com-1.4  32453  wl-impchain-com-2.3  32455