Theorem 19.21ad 741

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 704	. . 3 |- ((ph /\ ps) -> A.x(ph /\ ps))
4		19.21ad.3	. . . 4 |- (ph -> (ps -> ch))
5	4	imp 277	. . 3 |- ((ph /\ ps) -> ch)
6	3, 5	19.21ai 740	. 2 |- ((ph /\ ps) -> A.xch)
7	6	exp 291	1 |- (ph -> (ps -> A.xch))

Syntax hints:   -> wi 2   /\ wa 196  A.wal 672

This theorem is referenced by:  eqs2 829  19.21adv 945  moexex 1058  r19.21ad 1261  tz7.49 2997  pssnn 3428  fiint 3445

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-an 198

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