Theorem hbnae-o 2179

Description: All variables are effectively bound in a distinct variable specifier. Lemma L19 in [Megill] p. 446 (p. 14 of the preprint). Version of hbnae 1955 using ax-10o 2139. (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
hbnae-o	⊢ (¬ ∀x x = y → ∀z ¬ ∀x x = y)

Proof of Theorem hbnae-o

Step	Hyp	Ref	Expression
1		hbae-o 2153	. 2 ⊢ (∀x x = y → ∀z∀x x = y)
2	1	hbn 1776	1 ⊢ (¬ ∀x x = y → ∀z ¬ ∀x x = y)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-4 2135  ax-5o 2136  ax-6o 2137  ax-10o 2139  ax-12o 2142

This theorem depends on definitions:  df-bi 177  df-ex 1542

This theorem is referenced by:  dvelimf-o  2180  ax11indalem  2197  ax11inda2ALT  2198