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Theorem 19.27h 1449
Description: Theorem 19.27 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
19.27h.1 (ψxψ)
Assertion
Ref Expression
19.27h (x(φ ψ) ↔ (xφ ψ))

Proof of Theorem 19.27h
StepHypRef Expression
1 19.26 1367 . 2 (x(φ ψ) ↔ (xφ xψ))
2 19.27h.1 . . . 4 (ψxψ)
3219.3h 1442 . . 3 (xψψ)
43anbi2i 430 . 2 ((xφ xψ) ↔ (xφ ψ))
51, 4bitri 173 1 (x(φ ψ) ↔ (xφ ψ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98  wal 1240
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-4 1397
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  aaanh  1475  19.27v  1776
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