Theorem syl2an2 558

Description: syl2an 283 with antecedents in standard conjunction form. (Contributed by Alan Sare, 27-Aug-2016.)

Hypotheses

Ref	Expression
syl2an2.1	|- ( ph -> ps )
syl2an2.2	|- ( ( ch /\ ph ) -> th )
syl2an2.3	|- ( ( ps /\ th ) -> ta )

Assertion

Ref	Expression
syl2an2	|- ( ( ch /\ ph ) -> ta )

Proof of Theorem syl2an2

Step	Hyp	Ref	Expression
1		syl2an2.1	. . 3 |- ( ph -> ps )
2		syl2an2.2	. . 3 |- ( ( ch /\ ph ) -> th )
3		syl2an2.3	. . 3 |- ( ( ps /\ th ) -> ta )
4	1, 2, 3	syl2an 283	. 2 |- ( ( ph /\ ( ch /\ ph ) ) -> ta )
5	4	anabss7 547	1 |- ( ( ch /\ ph ) -> ta )

Syntax hints:   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  divalgmod  10327  gcdsupex  10349  gcdsupcl  10350  cncongr2  10486  isprm3  10500