Theorem nd5 4942

Description: A lemma for proving conditionless ZFC axioms.

Assertion

Ref	Expression
nd5	|- (-. A.y y = x -> (z = y -> A.x z = y))

Distinct variable group:   x,z

Proof of Theorem nd5

Step	Hyp	Ref	Expression
1		dveeq2 1212	. 2 |- (-. A.x x = y -> (z = y -> A.x z = y))
2	1	nalequcoms 1144	1 |- (-. A.y y = x -> (z = y -> A.x z = y))

Syntax hints:  -. wn 2   -> wi 3  A.wal 954   = wceq 956

This theorem is referenced by:  axrepndlem1 4944  axrepndlem2 4945  axunnd 4948  axpowndlem2 4950  axpowndlem4 4952  axregndlem2 4955  axinfndlem1 4957  axinfnd 4958  axacndlem4 4962  axacndlem5 4963  axacnd 4964

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140

This theorem depends on definitions:  df-bi 147  df-an 225

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