Theorem ja 137

Description: Inference joining the antecedents of two premises. (The proof was shortened by O'Cat, 19-Feb-2008.)

Hypotheses

Ref	Expression
ja.1	|- (-. ph -> ch)
ja.2	|- (ps -> ch)

Assertion

Ref	Expression
ja	|- ((ph -> ps) -> ch)

Proof of Theorem ja

Step	Hyp	Ref	Expression
1		ja.2	. . 3 |- (ps -> ch)
2	1	imim2i 17	. 2 |- ((ph -> ps) -> (ph -> ch))
3		ja.1	. 2 |- (-. ph -> ch)
4	2, 3	pm2.61d1 128	1 |- ((ph -> ps) -> ch)

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  pm2.74 571  pm5.71 746  hbim 1004  ax46 1013  ax467 1019  hbimd 1106  sbi2 1228  mo2 1393

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

Copyright terms: Public domain