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Theorem hba1-o 2207
Description:  x is not free in  A. x ph. Example in Appendix in [Megill] p. 450 (p. 19 of the preprint). Also Lemma 22 of [Monk2] p. 114. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.)
Assertion
Ref Expression
hba1-o  |-  ( A. x ph  ->  A. x A. x ph )

Proof of Theorem hba1-o
StepHypRef Expression
1 ax-4 2193 . . 3  |-  ( A. x  -.  A. x ph  ->  -.  A. x ph )
21con2i 114 . 2  |-  ( A. x ph  ->  -.  A. x  -.  A. x ph )
3 ax6 2205 . 2  |-  ( -. 
A. x  -.  A. x ph  ->  A. x  -.  A. x  -.  A. x ph )
4 ax6 2205 . . . 4  |-  ( -. 
A. x ph  ->  A. x  -.  A. x ph )
54con1i 123 . . 3  |-  ( -. 
A. x  -.  A. x ph  ->  A. x ph )
65alimi 1565 . 2  |-  ( A. x  -.  A. x  -.  A. x ph  ->  A. x A. x ph )
72, 3, 63syl 19 1  |-  ( A. x ph  ->  A. x A. x ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1546
This theorem is referenced by:  a5i-o  2208  nfa1-o  2224  ax67to6  2225  ax467to6  2229  dvelimf-o  2238  ax11indalem  2255  ax11inda2ALT  2256  ax11inda  2258
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-4 2193  ax-5o 2194  ax-6o 2195
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