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Theorem equidq 2175
Description: equid 1676 with universal quantifier without using ax-4 2135 or ax-17 1616. (Contributed by NM, 13-Jan-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
equidq y x = x

Proof of Theorem equidq
StepHypRef Expression
1 equidqe 2173 . 2 ¬ y ¬ x = x
2 ax6 2147 . . 3 y x = xy ¬ y x = x)
3 hbequid 2160 . . . 4 (x = xy x = x)
43con3i 127 . . 3 y x = x → ¬ x = x)
52, 4alrimih 1565 . 2 y x = xy ¬ x = x)
61, 5mt3 171 1 y x = x
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  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-4 2135  ax-5o 2136  ax-6o 2137  ax-9o 2138  ax-12o 2142
This theorem is referenced by: (None)
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