Theorem chv2 850

Description: Implicit substitution of y for x into a theorem. (Contributed by Raph Levien, 9-Jul-03.)

Hypotheses

Ref	Expression
chv2.1	⊢ (ψ → ∀xψ)
chv2.2	⊢ (x = y → (φ ↔ ψ))
chv2.3	⊢ φ

Assertion

Ref	Expression
chv2	⊢ ψ

Proof of Theorem chv2

Step	Hyp	Ref	Expression
1		chv2.1	. . 3 ⊢ (ψ → ∀xψ)
2		chv2.2	. . . 4 ⊢ (x = y → (φ ↔ ψ))
3	2	biimpd 135	. . 3 ⊢ (x = y → (φ → ψ))
4	1, 3	a4a 842	. 2 ⊢ (∀xφ → ψ)
5		chv2.3	. 2 ⊢ φ
6	4, 5	mpg 684	1 ⊢ ψ

Syntax hints:   → wi 2   ↔ wb 127  ∀wal 672   = weq 797

This theorem is referenced by:  tfis 2245  findes 2400  tfindes 2404  cnvopab 2632  tz6.12f 2844  dom2d 3307

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677  ax-9 799

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

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