Theorem bnj232 12075

Description: /\-manipulation.

Hypotheses

Ref	Expression
bnj232.1	|- (ph -> ph')
bnj232.2	|- (ps -> ps')

Assertion

Ref	Expression
bnj232	|- ((ph /\ ps) -> (ps' /\ ph'))

Proof of Theorem bnj232

Step	Hyp	Ref	Expression
1		bnj232.2	. . 3 |- (ps -> ps')
2		bnj232.1	. . 3 |- (ph -> ph')
3	1, 2	anim12i 360	. 2 |- ((ps /\ ph) -> (ps' /\ ph'))
4	3	ancoms 484	1 |- ((ph /\ ps) -> (ps' /\ ph'))

Syntax hints:   -> wi 3   /\ wa 240

This theorem is referenced by:  bnj933 12839  bnj545 13271  bnj1100 13414

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