Theorem sylan9OLD 518

Description: Nested syllogism inference conjoining dissimilar antecedents.

Hypotheses

Ref	Expression
sylan9.1	|- (ph -> (ps -> ch))
sylan9.2	|- (th -> (ch -> ta))

Assertion

Ref	Expression
sylan9OLD	|- ((ph /\ th) -> (ps -> ta))

Proof of Theorem sylan9OLD

Step	Hyp	Ref	Expression
1		sylan9.1	. . 3 |- (ph -> (ps -> ch))
2	1	adantr 425	. 2 |- ((ph /\ th) -> (ps -> ch))
3		sylan9.2	. . 3 |- (th -> (ch -> ta))
4	3	adantl 424	. 2 |- ((ph /\ th) -> (ch -> ta))
5	2, 4	syld 30	1 |- ((ph /\ th) -> (ps -> ta))

Syntax hints:   -> wi 3   /\ wa 240

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

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