Metamath Proof Explorer


Theorem syl6com

Description: Syllogism inference with commuted antecedents. (Contributed by NM, 25-May-2005)

Ref Expression
Hypotheses syl6com.1
|- ( ph -> ( ps -> ch ) )
syl6com.2
|- ( ch -> th )
Assertion syl6com
|- ( ps -> ( ph -> th ) )

Proof

Step Hyp Ref Expression
1 syl6com.1
 |-  ( ph -> ( ps -> ch ) )
2 syl6com.2
 |-  ( ch -> th )
3 1 2 syl6
 |-  ( ph -> ( ps -> th ) )
4 3 com12
 |-  ( ps -> ( ph -> th ) )