Theorem bnj240 30765

Description: /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Hypotheses

Ref	Expression
bnj240.1	|- ( ps -> ps' )
bnj240.2	|- ( ch -> ch' )

Assertion

Ref	Expression
bnj240	|- ( ( ph /\ ps /\ ch ) -> ( ps' /\ ch' ) )

Proof of Theorem bnj240

Step	Hyp	Ref	Expression
1		bnj240.1	. . . 4 |- ( ps -> ps' )
2	1	3ad2ant1 1082	. . 3 |- ( ( ps /\ ch /\ ph ) -> ps' )
3		bnj240.2	. . . 4 |- ( ch -> ch' )
4	3	3ad2ant2 1083	. . 3 |- ( ( ps /\ ch /\ ph ) -> ch' )
5	2, 4	jca 554	. 2 |- ( ( ps /\ ch /\ ph ) -> ( ps' /\ ch' ) )
6	5	3comr 1273	1 |- ( ( ph /\ ps /\ ch ) -> ( ps' /\ ch' ) )

Syntax hints:   -> wi 4   /\ wa 384   /\ w3a 1037

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1039

This theorem is referenced by:  bnj594  30982  bnj580  30983  bnj966  31014  bnj967  31015