Theorem 2a1d 23

Description: Deduction introducing two antecedents. Two applications of a1d 22. Deduction associated with 2a1 25 and 2a1i 27. (Contributed by BJ, 10-Aug-2020.)

Hypothesis

Ref	Expression
2a1d.1	|- ( ph -> ps )

Assertion

Ref	Expression
2a1d	|- ( ph -> ( ch -> ( th -> ps ) ) )

Proof of Theorem 2a1d

Step	Hyp	Ref	Expression
1		2a1d.1	. . 3 |- ( ph -> ps )
2	1	a1d 22	. 2 |- ( ph -> ( th -> ps ) )
3	2	a1d 22	1 |- ( ph -> ( ch -> ( th -> ps ) ) )

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:  2a1  25  ad5ant125  1272  nn0o1gt2  12672  lgsprme0  16161  gausslemma2dlem0i  16176  2lgsoddprm  16232