Theorem pm10.542

Description: Theorem *10.542 in WhiteheadRussell p. 156. (Contributed by Andrew Salmon, 24-May-2011)

	Ref	Expression
Assertion	pm10.542	|- ( A. x ( ph -> ( ch -> ps ) ) <-> ( ch -> A. x ( ph -> ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		bi2.04	|- ( ( ph -> ( ch -> ps ) ) <-> ( ch -> ( ph -> ps ) ) )
2	1	albii	|- ( A. x ( ph -> ( ch -> ps ) ) <-> A. x ( ch -> ( ph -> ps ) ) )
3		19.21v	|- ( A. x ( ch -> ( ph -> ps ) ) <-> ( ch -> A. x ( ph -> ps ) ) )
4	2 3	bitri	|- ( A. x ( ph -> ( ch -> ps ) ) <-> ( ch -> A. x ( ph -> ps ) ) )