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 ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  ssprsseq  3835  elpr2elpr  3859  elovmporab  6221  elovmporab1w  6222  updjud  7280  pfxccatin12  11313  alzdvds  12414  pcmptcl  12914  fiinopn  14727  cnmptcom  15021  metcnp3  15234  ausgrusgrben  16018  usgredg4  16065