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Theorem qlaxr4i 22156
Description: One of the conditions showing  CH is an ortholattice. (This corresponds to axiom "ax-r4" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004.) (New usage is discouraged.)
Hypotheses
Ref Expression
qlaxr4.1  |-  A  e. 
CH
qlaxr4.2  |-  B  e. 
CH
qlaxr4.3  |-  A  =  B
Assertion
Ref Expression
qlaxr4i  |-  ( _|_ `  A )  =  ( _|_ `  B )

Proof of Theorem qlaxr4i
StepHypRef Expression
1 qlaxr4.3 . 2  |-  A  =  B
21fveq2i 5426 1  |-  ( _|_ `  A )  =  ( _|_ `  B )
Colors of variables: wff set class
Syntax hints:    = wceq 1619    e. wcel 1621   ` cfv 4638   CHcch 21434   _|_cort 21435
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2237
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-rex 2521  df-rab 2523  df-v 2742  df-dif 3097  df-un 3099  df-in 3101  df-ss 3108  df-nul 3398  df-if 3507  df-sn 3587  df-pr 3588  df-op 3590  df-uni 3769  df-br 3964  df-opab 4018  df-xp 4640  df-cnv 4642  df-dm 4644  df-rn 4645  df-res 4646  df-ima 4647  df-fv 4654
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