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Theorem 19.21 1796
 Description: Theorem 19.21 of [Margaris] p. 90. The hypothesis can be thought of as "x is not free in φ." (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.)
Hypothesis
Ref Expression
19.21.1 xφ
Assertion
Ref Expression
19.21 (x(φψ) ↔ (φxψ))

Proof of Theorem 19.21
StepHypRef Expression
1 19.21.1 . 2 xφ
2 19.21t 1795 . 2 (Ⅎxφ → (x(φψ) ↔ (φxψ)))
31, 2ax-mp 8 1 (x(φψ) ↔ (φxψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀wal 1540  Ⅎwnf 1544 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545 This theorem is referenced by:  19.21h  1797  stdpc5  1798  nfim1OLD  1812  19.21-2  1864  nf3  1867  19.32  1875  19.21v  1890  19.12vv  1898  ax15  2021  eu2  2229  moanim  2260  r2alf  2649
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