Theorem hband 788

Description: Deduction form of bound-variable hypothesis builder hban 704.

Hypotheses

Ref	Expression
hband.1	|- (ph -> (ps -> A.xps))
hband.2	|- (ph -> (ch -> A.xch))

Assertion

Ref	Expression
hband	|- (ph -> ((ps /\ ch) -> A.x(ps /\ ch)))

Proof of Theorem hband

Step	Hyp	Ref	Expression
1		hband.1	. . 3 |- (ph -> (ps -> A.xps))
2		hband.2	. . 3 |- (ph -> (ch -> A.xch))
3	1, 2	anim12d 431	. 2 |- (ph -> ((ps /\ ch) -> (A.xps /\ A.xch)))
4		19.26 749	. 2 |- (A.x(ps /\ ch) <-> (A.xps /\ A.xch))
5	3, 4	syl6ibr 186	1 |- (ph -> ((ps /\ ch) -> A.x(ps /\ ch)))

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

This theorem is referenced by:  axrepndlem1 3738  axrepndlem2 3739  axunndlem1 3741  axunnd 3742  axregndlem2 3749  axinfndlem1 3751  axinfnd 3752  axacndlem4 3756  axacndlem5 3757  axacnd 3758

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-gen 677

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

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