Theorem del44 878

Description: A distinctor elimination lemma for substitution.

Assertion

Ref	Expression
del44	⊢ (∀x x = y → ([x / z]φ → [y / z]φ))

Proof of Theorem del44

Step	Hyp	Ref	Expression
1		sbequi 876	. 2 ⊢ (x = y → ([x / z]φ → [y / z]φ))
2	1	a4s 682	1 ⊢ (∀x x = y → ([x / z]φ → [y / z]φ))

Syntax hints:   → wi 2  ∀wal 672   = weq 797  [wsb 852

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-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853

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