Theorem syl11 31

Description: A syllogism inference. Commuted form of an instance of syl 14. (Contributed by BJ, 25-Oct-2021.)

Hypotheses

Ref	Expression
syl11.1	|- ( ph -> ( ps -> ch ) )
syl11.2	|- ( th -> ph )

Assertion

Ref	Expression
syl11	|- ( ps -> ( th -> ch ) )

Proof of Theorem syl11

Step	Hyp	Ref	Expression
1		syl11.2	. . 3 |- ( th -> ph )
2		syl11.1	. . 3 |- ( ph -> ( ps -> ch ) )
3	1, 2	syl 14	. 2 |- ( th -> ( ps -> ch ) )
4	3	com12 30	1 |- ( ps -> ( th -> ch ) )

This proof depends on syntax axioms:   -> wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by:  ssprsseq  3877  elpr2elpr  3901  elovmporab  6289  elovmporab1w  6290  updjud  7422  pfxccatin12  11505  alzdvds  12621  pcmptcl  13121  fiinopn  15105  cnmptcom  15399  metcnp3  15612  ausgrusgrben  16409  usgredg4  16456