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Theorem hbald 1377
Description: Deduction form of bound-variable hypothesis builder hbal 1363. (Contributed by NM, 2-Jan-2002.)
Hypotheses
Ref Expression
hbald.1 (φyφ)
hbald.2 (φ → (ψxψ))
Assertion
Ref Expression
hbald (φ → (yψxyψ))

Proof of Theorem hbald
StepHypRef Expression
1 hbald.1 . . 3 (φyφ)
2 hbald.2 . . 3 (φ → (ψxψ))
31, 2alimdh 1353 . 2 (φ → (yψyxψ))
4 ax-7 1334 . 2 (yxψxyψ)
53, 4syl6 29 1 (φ → (yψxyψ))
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-7 1334  ax-gen 1335
This theorem is referenced by:  nfald  1640  dvelimfALT2  1695
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