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Theorem ax11f 2192
Description: Basis step for constructing a substitution instance of ax-11o 2141 without using ax-11o 2141. We can start with any formula φ in which x is not free. (Contributed by NM, 21-Jan-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
ax11f.1 (φxφ)
Assertion
Ref Expression
ax11f x x = y → (x = y → (φx(x = yφ))))

Proof of Theorem ax11f
StepHypRef Expression
1 ax11f.1 . . 3 (φxφ)
2 ax-1 6 . . 3 (φ → (x = yφ))
31, 2alrimih 1565 . 2 (φx(x = yφ))
432a1i 24 1 x x = y → (x = y → (φx(x = yφ))))
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-gen 1546  ax-5 1557
This theorem is referenced by: (None)
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