Theorem syl9 72

Description: A nested syllogism inference with different antecedents. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.)

Hypotheses

Ref	Expression
syl9.1	|- ( ph -> ( ps -> ch ) )
syl9.2	|- ( th -> ( ch -> ta ) )

Assertion

Ref	Expression
syl9	|- ( ph -> ( th -> ( ps -> ta ) ) )

Proof of Theorem syl9

Step	Hyp	Ref	Expression
1		syl9.1	. 2 |- ( ph -> ( ps -> ch ) )
2		syl9.2	. . 3 |- ( th -> ( ch -> ta ) )
3	2	a1i 9	. 2 |- ( ph -> ( th -> ( ch -> ta ) ) )
4	1, 3	syl5d 68	1 |- ( ph -> ( th -> ( ps -> ta ) ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  syl9r  73  com23  78  sylan9  406  pm4.79dc  888  pclem6  1352  bilukdc  1374  sbequi  1811  reuss2  3351  reupick  3355  elres  4850  funimass4  5465  fliftfun  5690  elabgf2  12976  bj-rspgt  12982