Theorem syldanl 15649

Description: A syllogism deduction with conjoined antecedents.

Hypotheses

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

Assertion

Ref	Expression
syldanl	|- (((ph /\ ps) /\ th) -> ta)

Proof of Theorem syldanl

Step	Hyp	Ref	Expression
1		syldanl.2	. 2 |- (((ph /\ ch) /\ th) -> ta)
2		syldanl.1	. . . 4 |- ((ph /\ ps) -> ch)
3	2	ex 402	. . 3 |- (ph -> (ps -> ch))
4	3	imdistani 491	. 2 |- ((ph /\ ps) -> (ph /\ ch))
5	1, 4	sylan 497	1 |- (((ph /\ ps) /\ th) -> ta)

Syntax hints:   -> wi 3   /\ wa 240

This theorem is referenced by:  idlnegcl 16170  igenmin 16212

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164  df-an 242

Copyright terms: Public domain