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Theorem wl-equsal1i 31376
 Description: The antecedent is irrelevant, if one or both setvar variables are not free in . (Contributed by Wolf Lammen, 1-Sep-2018.)
Hypotheses
Ref Expression
wl-equsal1i.1
wl-equsal1i.2
Assertion
Ref Expression
wl-equsal1i

Proof of Theorem wl-equsal1i
StepHypRef Expression
1 wl-equsal1i.1 . 2
2 wl-equsal1i.2 . . 3
32gen2 1642 . 2
4 sp 1885 . . . . 5
54alcoms 1869 . . . 4
6 wl-equsal1t 31374 . . . 4
75, 6syl5ib 221 . . 3
8 wl-equsalcom 31375 . . . . 5
9 wl-equsal1t 31374 . . . . . 6
109biimpd 209 . . . . 5
118, 10syl5bir 220 . . . 4
1211spsd 1893 . . 3
137, 12jaoi 379 . 2
141, 3, 13mp2 9 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wo 368  wal 1405  wnf 1639 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-10 1863  ax-11 1868  ax-12 1880  ax-13 2028 This theorem depends on definitions:  df-bi 187  df-or 370  df-an 371  df-ex 1636  df-nf 1640 This theorem is referenced by: (None)
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