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Theorem ax4sp1 2174
Description: A special case of ax-4 2135 without using ax-4 2135 or ax-17 1616. (Contributed by NM, 13-Jan-2011.) (Proof modification is discouraged.)
Assertion
Ref Expression
ax4sp1 (y ¬ x = x → ¬ x = x)

Proof of Theorem ax4sp1
StepHypRef Expression
1 equidqe 2173 . 2 ¬ y ¬ x = x
21pm2.21i 123 1 (y ¬ x = x → ¬ x = x)
Colors of variables: wff setvar class
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-8 1675  ax-6o 2137  ax-9o 2138
This theorem is referenced by: (None)
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