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Theorem w2an 373
Description: Join both sides with conjunction.
Hypotheses
Ref Expression
w2an.1 (a == b) = 1
w2an.2 (c == d) = 1
Assertion
Ref Expression
w2an ((a ^ c) == (b ^ d)) = 1
Proof of Theorem w2an
StepHypRef Expression
1 w2an.2 . . 3 (c == d) = 1
21wlan 370 . 2 ((a ^ c) == (a ^ d)) = 1
3 w2an.1 . . 3 (a == b) = 1
43wran 369 . 2 ((a ^ d) == (b ^ d)) = 1
52, 4wr2 371 1 ((a ^ c) == (b ^ d)) = 1
Colors of variables: term
Syntax hints:   = wb 1   == tb 5   ^ wa 7  1wt 8
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-wom 361
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-le1 130  df-le2 131
This theorem is referenced by:  wcomd  418  wcom3ii  419  wcomcom5  420  wfh1  423  wfh3  425  wfh4  426  wddi4  1108  wdid0id5  1109  wdid0id1  1110  wdid0id2  1111
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