Theorem syland 457

Description: A syllogism deduction.

Hypotheses

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

Assertion

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

Proof of Theorem syland

Step	Hyp	Ref	Expression
1		syland.2	. . 3 |- (ph -> (ta -> ps))
2		syland.1	. . . 4 |- (ph -> ((ps /\ ch) -> th))
3	2	exp3a 375	. . 3 |- (ph -> (ps -> (ch -> th)))
4	1, 3	syld 27	. 2 |- (ph -> (ta -> (ch -> th)))
5	4	imp3a 361	1 |- (ph -> ((ta /\ ch) -> th))

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  sylan2d 458  syl2and 459  sylani 464  seqzrn 6557

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 147  df-an 225

Copyright terms: Public domain