Theorem 19.21ad 1055

Description: Deduction from Theorem 19.21 of [Margaris] p. 90.

Hypotheses

Ref	Expression
19.21ad.1	|- (ph -> A.xph)
19.21ad.2	|- (ps -> A.xps)
19.21ad.3	|- (ph -> (ps -> ch))

Assertion

Ref	Expression
19.21ad	|- (ph -> (ps -> A.xch))

Proof of Theorem 19.21ad

Step	Hyp	Ref	Expression
1		19.21ad.1	. . . 4 |- (ph -> A.xph)
2		19.21ad.2	. . . 4 |- (ps -> A.xps)
3	1, 2	hban 1006	. . 3 |- ((ph /\ ps) -> A.x(ph /\ ps))
4		19.21ad.3	. . . 4 |- (ph -> (ps -> ch))
5	4	imp 350	. . 3 |- ((ph /\ ps) -> ch)
6	3, 5	19.21ai 995	. 2 |- ((ph /\ ps) -> A.xch)
7	6	ex 373	1 |- (ph -> (ps -> A.xch))

Syntax hints:   -> wi 3   /\ wa 223  A.wal 951

This theorem is referenced by:  19.21adv 1283  ax11indn 1359  a12study 1371  moexex 1431  r19.21ad 1709  alxfr 2886  tz7.49 3944  pssnn 4513  fiint 4534  islp2 7688

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 960  ax-4 970  ax-5o 972  ax-6o 975

This theorem depends on definitions:  df-bi 147  df-an 225

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