Theorem wl-impchain-com-3.2.1 34739

Description: This theorem is in fact a copy of com3r 87. The proof is an example of how to arrive at arbitrary permutations of antecedents, using only swapping theorems. The recursion principle is to first swap the correct antecedent to the position just before the consequent, and then employ a theorem handling an implication chain of length one less to reorder the others. (Contributed by Wolf Lammen, 17-Nov-2019.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
wl-impchain-com-3.2.1.h1	⊢ (𝜃 → (𝜒 → (𝜓 → 𝜑)))

Assertion

Ref	Expression
wl-impchain-com-3.2.1	⊢ (𝜓 → (𝜃 → (𝜒 → 𝜑)))

Proof of Theorem wl-impchain-com-3.2.1

Step	Hyp	Ref	Expression
1		wl-impchain-com-3.2.1.h1	. . 3 ⊢ (𝜃 → (𝜒 → (𝜓 → 𝜑)))
2	1	wl-impchain-com-2.3 34737	. 2 ⊢ (𝜃 → (𝜓 → (𝜒 → 𝜑)))
3	2	wl-impchain-com-1.2 34733	1 ⊢ (𝜓 → (𝜃 → (𝜒 → 𝜑)))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 34699  ax-luk2 34700  ax-luk3 34701

This theorem is referenced by: (None)