Metamath Proof Explorer


Theorem wl-impchain-mp-1

Description: This theorem is in fact a copy of wl-luk-syl , and repeated here to demonstrate a recursive proof scheme. The number '1' in the theorem name indicates that a chain of length 1 is modified. (Contributed by Wolf Lammen, 6-Jul-2019) (New usage is discouraged.) (Proof modification is discouraged.)

Ref Expression
Hypotheses wl-impchain-mp-1.a
|- ( ch -> ps )
wl-impchain-mp-1.b
|- ( ps -> ph )
Assertion wl-impchain-mp-1
|- ( ch -> ph )

Proof

Step Hyp Ref Expression
1 wl-impchain-mp-1.a
 |-  ( ch -> ps )
2 wl-impchain-mp-1.b
 |-  ( ps -> ph )
3 2 wl-luk-imim2i
 |-  ( ( ch -> ps ) -> ( ch -> ph ) )
4 1 3 wl-impchain-mp-0
 |-  ( ch -> ph )