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Theorem 19.42h 1555
 Description: Theorem 19.42 of [Margaris] p. 90. New proofs should use 19.42 1556 instead. (Contributed by NM, 18-Aug-1993.) (New usage is discouraged.)
Hypothesis
Ref Expression
19.42h.1 (φxφ)
Assertion
Ref Expression
19.42h (x(φ ψ) ↔ (φ xψ))

Proof of Theorem 19.42h
StepHypRef Expression
1 19.42h.1 . . 3 (φxφ)
2119.41h 1553 . 2 (x(ψ φ) ↔ (xψ φ))
3 exancom 1477 . 2 (x(φ ψ) ↔ x(ψ φ))
4 ancom 253 . 2 ((φ xψ) ↔ (xψ φ))
52, 3, 43bitr4i 201 1 (x(φ ψ) ↔ (φ xψ))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ↔ wb 98  ∀wal 1224  ∃wex 1358 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 1312  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-4 1377  ax-ial 1405 This theorem depends on definitions:  df-bi 110 This theorem is referenced by:  19.42v  1764
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