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Theorem hbimd 1462
Description: Deduction form of bound-variable hypothesis builder hbim 1434. (Contributed by NM, 1-Jan-2002.) (Revised by NM, 2-Feb-2015.)
Hypotheses
Ref Expression
hbimd.1 (φxφ)
hbimd.2 (φ → (ψxψ))
hbimd.3 (φ → (χxχ))
Assertion
Ref Expression
hbimd (φ → ((ψχ) → x(ψχ)))

Proof of Theorem hbimd
StepHypRef Expression
1 hbimd.3 . . . 4 (φ → (χxχ))
21imim2d 48 . . 3 (φ → ((ψχ) → (ψxχ)))
3 ax-4 1397 . . . . 5 (xψψ)
43imim1i 54 . . . 4 ((ψxχ) → (xψxχ))
5 ax-i5r 1425 . . . 4 ((xψxχ) → x(xψχ))
64, 5syl 14 . . 3 ((ψxχ) → x(xψχ))
72, 6syl6 29 . 2 (φ → ((ψχ) → x(xψχ)))
8 hbimd.1 . . 3 (φxφ)
9 hbimd.2 . . . 4 (φ → (ψxψ))
109imim1d 69 . . 3 (φ → ((xψχ) → (ψχ)))
118, 10alimdh 1353 . 2 (φ → (x(xψχ) → x(ψχ)))
127, 11syld 40 1 (φ → ((ψχ) → x(ψχ)))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1240
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1333  ax-gen 1335  ax-4 1397  ax-i5r 1425
This theorem is referenced by:  hbbid  1464  19.21ht  1470  equveli  1639  dvelimfALT2  1695
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