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Theorem chvar 1986
 Description: Implicit substitution of y for x into a theorem. (Contributed by Raph Levien, 9-Jul-2003.) (Revised by Mario Carneiro, 3-Oct-2016.)
Hypotheses
Ref Expression
chvar.1 xψ
chvar.2 (x = y → (φψ))
chvar.3 φ
Assertion
Ref Expression
chvar ψ

Proof of Theorem chvar
StepHypRef Expression
1 chvar.1 . . 3 xψ
2 chvar.2 . . . 4 (x = y → (φψ))
32biimpd 198 . . 3 (x = y → (φψ))
41, 3spim 1975 . 2 (xφψ)
5 chvar.3 . 2 φ
64, 5mpg 1548 1 ψ
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  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-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by:  csbhypf  3171  opelopabsb  4697
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