Theorem 2a1dd 51

Description: Double deduction introducing two antecedents. Two applications of 2a1dd 51. Deduction associated with 2a1d 26. Double deduction associated with 2a1 28 and 2a1i 12. (Contributed by Jeff Hankins, 5-Aug-2009.)

Hypothesis

Ref	Expression
2a1dd.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
2a1dd	|- ( ph -> ( ps -> ( th -> ( ta -> ch ) ) ) )

Proof of Theorem 2a1dd

Step	Hyp	Ref	Expression
1		2a1dd.1	. . 3 |- ( ph -> ( ps -> ch ) )
2	1	a1dd 50	. 2 |- ( ph -> ( ps -> ( ta -> ch ) ) )
3	2	a1dd 50	1 |- ( ph -> ( ps -> ( th -> ( ta -> ch ) ) ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  ad5ant13  1301  ad5ant14  1302  ad5ant15  1303  ad5ant23  1304  ad5ant24  1305  ad5ant25  1306  ad5ant125  1312