Theorem embantd 56

Description: Deduction embedding an antecedent. (Contributed by Wolf Lammen, 4-Oct-2013.)

Hypotheses

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

Assertion

Ref	Expression
embantd	|- ( ph -> ( ( ps -> ch ) -> th ) )

Proof of Theorem embantd

Step	Hyp	Ref	Expression
1		embantd.1	. 2 |- ( ph -> ps )
2		embantd.2	. . 3 |- ( ph -> ( ch -> th ) )
3	2	imim2d 54	. 2 |- ( ph -> ( ( ps -> ch ) -> ( ps -> th ) ) )
4	1, 3	mpid 42	1 |- ( ph -> ( ( ps -> ch ) -> th ) )

This proof depends on syntax axioms:   -> wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by:  a2and  564  el  4315  findcard2d  7195  findcard2sd  7196  exprmfct  12916  sqrt2irr  12940  pockthg  13136  iscnp4  15319  2sqlem6  16239  bj-exlimmp  16797