Theorem wl-jarli 33289

Description: Dropping a nested consequent. This theorem is one of two reversions of ja 173. Since ja 173 is reversible, one can conclude, that a nested (chain of) implication(s) is just a packed notation of two or more theorems/ hypotheses with a common consequent. axc5c7 34196 is an instance of this idea. (Contributed by Wolf Lammen, 4-Oct-2013.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
wl-jarli.1	|- ( ( ph -> ps ) -> ch )

Assertion

Ref	Expression
wl-jarli	|- ( -. ph -> ch )

Proof of Theorem wl-jarli

Step	Hyp	Ref	Expression
1		pm2.21 120	. 2 |- ( -. ph -> ( ph -> ps ) )
2		wl-jarli.1	. 2 |- ( ( ph -> ps ) -> ch )
3	1, 2	syl 17	1 |- ( -. ph -> ch )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by: (None)